Marys Medicine

[1] H. D. R. Arises.
Defeating AIDS: What will it [15] K. Aoki. Gene-culture waves of advance. J. Math. take? Sci. Amer., 279: 61–87, July 1998.
Biol., 25: 453–464, 1987.
[2] D. Aikman and G. Hewitt. An experimental in- and J. J. Tyson.
vestigation of the rate and form of dispersal in Propagation of chemical reactions in space.
grasshoppers. J. Appl. Ecol., 9: 807–817, 1972.
Chem. Educ., 64: 740–742, 1987. Translation of: [3] M. Alpert. Where have all the boys gone? Luther, R.-L.: Rauemliche Fortpflanzung Chemis- Amer., 279: 22–23, 1998.
cher Reaktionen. In: ur Elektrochemie und [4] W. Alt and D. A. Lauffenburger. Transient behav- angew. physikalische Chemie. vol. 1232, pp. 506– ior of a chemotaxis system modelling certain types of tissue inflamation. J. Math. Biol., 24: 691–722, [17] D. G. Aronson.
diffusion systems. In W. E. Stewart, W. H. Ray, [5] A. J. Ammerman and L. L. Cavalli-Sforza. Mea- and C. C. Conley, editors, Dynamics and Mod- suring the rate of spread of early farming. Man, 6: elling of Reactive Systems, pages 161–176. Aca- 674–688, 1971.
demic Press, New York, 1980.
[6] A. J. Ammerman and L. L. Cavalli-Sforza. The [18] J.-P. Aubin. Viability Theory. Birkh¨ Neolithic Transition and the Genetics of Popula- Basel-Berlin, 1991.
tions in Europe. Princeton University Press, NJ, [19] D. Avnir, O. Biham, D. Lidar, and O. Malcai. Is Princeton, 1983.
the geometry of nature fractal? Science, 279: 39– [7] R. A. Anderson, E. M. Wallace, N. P. Groome, A.
J. Bellis, and F. C. Wu. Physiological relationships [20] P. Bacchetti, M. R. Segal, and N. P. Jewell. Back- between inhibin B, follicle stimulating hormone se- calculation of HIV infection rates. Statist. Sci., 8: cretion and spermatogenesis in normal men and re- 82–101, 1993.
sponse to gonadotrophin suppression by exogenous [21] P. F. Baconnier, G. Benchetrit, P. Pachot, and testosterone. Human Reproduction, 12: 746–751, J. Demongeot.
Entrainment of the respiratory rhythm: a new approach. J. theor. Biol., 164: 149– [8] R. M. Anderson. The epidemiology of HIV infec- tion: variable incubation plus infectious periods [22] N. T. J. Bailey. The Mathematical Theory of In- and heterogeneity in sexual activity. J. Roy. Stat. fectious Diseases. Griffin, London, second edition, Soc. (A), 151: 66–93, 1988.
[9] R. M. Anderson and R. M. May. Directly trans- [23] D. Barkley, J. Ringland, and J. S. Turner. Ob- mitted infectious diseases: control by vaccination.
servations of a torus in a model for the Belousov- Science, 215: 1053–1060, 1982.
Zhabotinskii reaction. J. Chem. Phys., 87: 3812– [10] R. M. Anderson and R. M. May. Vaccination and herd immunity to infectious diseases. Nature, 318: [24] J. B. Bassingthwaighte, L. S. Liebovitch, and B. J.
323–329, 1985.
West. Fractal Physiology. Oxford University Press, [11] R. M. Anderson and R. M. May. The invasion, New York, 1994.
persistence and spread of infectious diseases within [25] M. T. Beck and Z. B. V´ aradi. One, two and three- animal and plant communities. Phil. Trans. Roy. dimensional spatially periodic chemical reactions.
Soc. Lond. B, 314: 533–570, 1986.
Nature, 235: 15–16, 1972.
[12] R. M. Anderson and R. M. May, editors. Infectious [26] J. R. Beddington, C. A. Free, and J. H. Law- Diseases of Humans: Dynamics and Control. Ox- ton. Dynamic complexity in predator-prey models ford University Press, Oxford, 1991.
framed in difference equations. Nature, 255: 58–60, [13] R. M. Anderson, G. F. Medley, R. M. May, and A. M. Johnson. A preliminary study of the trans- [27] J. R. Beddington and R. M. May. Harvesting natu- mission dynamics of the human immunodeficiency ral populations in a randomly fluctuating environ- virus (HIV), the causitive agent of AIDS. IMA J. ment. Science, 197: 463–465, 1977.
Maths. Appl. in Medicine and. Biol., 3: 229–263, [28] B. P. Belousov.
An oscillating reaction and its mechanism. In Sborn. referat. radiat. med. (Col- [14] R. M. Anderson and W. Trewhella.
lection of abstracts on radiation medicine), page dynamics of the badger (Meles meles) and the epi- 145. Medgiz, Moscow, 1959.
demiologyof bovine tuberculosis (Mycobacterium [29] B. P. Belousov. A periodic reaction and its mech- bovis). Phil. Trans. R. Soc. Lond. B, 310: 327– In R. J. Field and M. Burger, editors, Oscillations and Travelling Waves in Chemical Systems, 1951, (from his archives (in Russian)), Microbiol., 2: 43–46-8713, 1994.
pages 605–613. John Wiley, New York, 1985.
[49] BTEC. The Australian brucellosis and tubercu- [30] G. Benchetrit, P. Baconnier, and J. Demongeot.
losis eradication campaign. Technical Report 97, Concepts and Formalizations in the Control of AGPS, Canberra, 1987.
Breathing. Manchester University Press, Manch- [50] J. T. Buchanan and A. H. Cohen. Activities of ester, 1987.
identified interneurons, motorneurons, and muscle [31] L. M. Benedict, E. Abell, and B. Jegasothy. Telo- fibers during fictive swimming in the lamprey and gen effluvium associated with eosinophilia-myalgia effects of reticulospinal and dorsal cell stimulation.
A. American Acad. Dermatol., 25: J. of Neurophys., 47: 948–960, 1982.
112–114, 1991.
[51] J. Buck. Synchronous rhythmic flashing of fireflies.
[32] E. Benoit, J. L. Callot, F. Diener, and M. Diener.
II [published erratum appears in Q. Rev. Biol. 1989 Chasse au canard. Collectanea Mathematica, 32: Jun;64(2): 146]. Q. Rev. Biol., 63(3): 265–289, 37–119, 1981.
[33] D. E. Bentil and J. D. Murray. Pattern selection [52] J. Buck and E. Buck. Synchronous fireflies. Sci. in biological pattern formation mechanisms. Appl. Amer., 234(5): 74–79, 82–85, 1976.
Maths. Letters, 4: 1–5, 1991.
[53] M. A. Burke, P. K. Maini, and J. D. Murray. On [34] D. E. Bentil and J. D. Murray. Modelling bovine the kinetics of suicide substrates. Biophys. Chem., tuberculosis in badgers. J. Animal Ecol., 62: 239– 37: 81–90, 1990. Jeffries Wyman Anniversary Vol- [35] P. M. Bentler and M. D. Newcomb. Longitudinal [54] H. R. Bustard.
Breeding the gharial (Gavialis study of marriage success and failure. J. Consult- gangeticus): captive breeding a key conservation ing and Clinical Psychol., 46: 1053–1070, 1978.
strategy for endangered crocodiles. In The Struc- [36] M. J. Benton. Vertebrate Palaeontology. Chapman ture, Development and Evolution of Reptiles, vol- and Hall, London, 1997.
ume 52 of Symp. Zool. Soc. Lond., pages 385–406, [37] C. Berding.
On the heterogeneity of reaction- London, 1984. Academic Press.
diffusion generated patterns.
Bull. Math. Biol., [55] A. E. Butterworth, M. Kapron, J. S. Cordingley, 49: 233–252, 1987.
P. R. Dalton, D. W. Dunne, H. C. Kariuki, G. Ki- [38] C. Berding, A. E. Keymer, J. D. Murray, and A.
mani, D. Koech, M. Mugambi, J. H. Ouma, M. A.
F. G. Slater. The population dynamics of acquired Prentice, B. A. Richardson, T. K. Arap Siongok, immunity to helminth infections. J. theor. Biol., R. F. Sturrock, and D. W. Taylor. Immunity af- 122: 459–471, 1986.
ter treatment of human schistomiasis mansoni. II.
[39] C. Berding, A. E. Keymer, J. D. Murray, and A.
Identification of resistant individuals and analysis F. G. Slater.
The population dynamics of ac- of their immune responses. Trans. Roy. Soc. Trop. quired immunity to helminth infections: experi- Med. Hyg., 79: 393–408, 1985.
mental and natural infections. J. theor. Biol., 126: [56] J. W. Cahn.
Free energy of a non-uniform sys- 167–182, 1987.
tem. II. Thermodynamic basis. J. Chem. Phys., [40] D. Bernoulli. Essai d'une nouvelle analyse de la 30: 1121–1124, 1959.
ee par la petite v´ erole, et des avan- [57] J. W. Cahn and J. E. Hilliard. Free energy of a tages de l'inoculation pour la pr´ evenir. Histoire de non-uniform system. I. Interfacial free energy. J. l'Acad. Roy. Sci. (Paris) avec M´ em. des Math. et Chem. Phys., 28: 258–267, 1958.
Phys. and M´ em., pages 1–45, 1760.
[58] J. W. Cahn and J. E. Hilliard.
[41] E. N. Best.
Null space in the Hodgkin-Huxley a non-uniform system. III. Nucleation in a two- equations: a critical test. Biophys. J, 27: 87–104, component incompressible fluid. J. Chem. Phys., 31: 688–699, 1959.
[42] J. A. M. Borghans, R. J. DeBoer, and L. A. Segel.
[59] J. Canosa. On a nonlinear diffusion equation de- Extending the quasi-steady state approximation scribing population growth. IBM J. Res. and Dev., by changing variables. Bull. Math. Biol., 58: 43– 17: 307–313, 1973.
[60] V. Capasso and S. L. Paveri-Fontana. A mathe- [43] F. Brauer and D. A. Sanchez. Constant rate popu- matical model for the 1973 cholera epidemic in the lation harvesting: equilibrium and stability. Theor. European Mediterranean region. Rev. Epid´ Population Biol., 8: 12–30, 1975.
e Publ., 27: 121–132, 1979.
[44] W. C. Bray. A periodic reaction in homogeneous [61] C. Carelli, F. Audibert, J. Gaillard, and L. Che- solution and its relation to catalysis.
Immunological castration of male mice by Chem. Soc., 43: 1262–1267, 1921.
a totally synthetic vaccine administered in saline.
[45] N. F. Britton. Reaction-Diffusion Equations and Proc. Nat. Acad. Sci. U.S.A., 79: 5392–5395, 1982.
their Applications to Biology. Academic Press, [62] R. L. Carroll. Vertebrate Palaeontology and Evo- New York, 1986.
lution. Freeman, New York, 1988.
[46] N. F. Britton and J. D. Murray.
[63] M. Cartwright and M. A. Husain. A model for the carbon monoxide on haem-facilitated oxygen dif- control of testosterone secretion. J. theor. Biol., fusion. Biophys. Chem., 7: 159–167, 1977.
123: 239–250, 1986.
[47] M. Brons and K. Bar-Eli. Canard explosion and [64] F. Caserta, H. E. Stanley, W. D. Eldred, G. Dac- excitation in a model of the Belousov-Zhabotinsky cord, R. E. Hausman, and J. Nittman. Physical reaction. J. Physical Chem., 95: 8706–8713, 1991.
mechanism underlying neurite outgrowth: a quan- [48] J. A. Brown, S. Harris, and P. C. L. White. Per- titative analysis of neuronal shape.
Phys. Rev. sistence of mycobacterium bovis in cattle. Trends Lett., 64: 95–98, 1990.
[65] H. Caswell, editor.
Matrix Population Models: through Time. Wiley and Liss, New York, 1991.
Construction, Analysis, and Interpretation. Sin- auer Associates, Sunderland, MA, 1989.
[84] L. C. Cole. The population consequences of life [66] B. Charlesworth. Evolution in Age-structured Pop- history phenomena. Q. Rev. Biol., 29: 103–137, ulations. Cambridge University Press, Cambridge, [85] H. Connor, H. F. Woods, J. G. G. Ledingham, and [67] E. L. Charnov and J. Bull. When is sex environ- J. D. Murray. A model of L+ lactate metabolism in mentally determined? Nature, 266: 828–830, 1977.
normal man. Annals of Nutrition and Metabolism, [68] A. Cheer, R. Nuccitelli, G. F. Oster, and J.-P. Vin- 26: 254–263, 1982a.
cent. Cortical activity in vertebrate eggs I: The [86] H. Connor, H. F. Woods, J. D. Murray, and J. G.
activation waves.
J. theor. Biol., 124: 377–404, G. Ledingham.
Utilisation of L+ lactate in pa- tients with liver disease. Annals of Nutrition and [69] C. L. Cheeseman, Wilesmith J. W. , and F. A. Stu- Metabolism, 26: 308–314, 1982b.
art. Tuberculosis: the disease and its epidemiology [87] J. Cook, R. C. Tyson, J. White, R. Rushe, J.
in the badger, a review. Epid. Inf., 103: 113–125, Gottman, and J. D. Murray. Mathematics of mar- qualitative dynamic mathematical [70] C. L. Cheeseman, Wilesmith J. W. , F. A. Stuart, modeling of marital interaction. J. Family Psy- and P. J. Mallinson. Dynamics of tuberculosis in chology, 9: 110–130, 1995.
a naturally infected badger population. Mammal [88] O. Cosivi, J. M. Grange, C. J. Daborn, et al.
Review, 18: 61–72, 1988.
Zoonotic tuberculosis due to Mycobacterium bo- [71] C. W. Clark. Mathematical Bioeconomics, the op- vis in developing countries. Emerging Infectious timal control of renewable resources. John Wiley, Diseases, 4: 59–69, 1998.
New York, 1976a.
[89] M. Cosnard and J. Demongeot. Attracteurs: une eterministe. C. R. Acad. Sci., 300: 551– [72] C. W. Clark. A delayed-recruitment model of pop- ulation dynamics with an application to baleen [90] J. Crank. The Mathematics of Diffusion. Claren- whale populations.
J. Math. Biol., 3: 381–391, don Press, Oxford, 1975.
[91] S. S. Cross. The application of fractal geometric [73] C. W. Clark. Bioeconomics Modeling and Fishery analysis to microscopic images. Micron, 1: 101– Management. Wiley Interscience, New York, 1985.
[92] S. S. Cross and D. W. K. Cotton. Chaos and an- tichaos in pathology. Human Pathol., 25: 630–637, [74] C. W. Clark. Mathematical Bioeconomics. John Wiley, New York, 1990.
[93] P. Cvitanovi´ Universality in Chaos.
[75] E. D. Clements, E. G. Neal, and D. W. Yalden.
Hilger, Bristol, 1984.
The national badger sett survey. Mammal Review, [94] C. J. Daborn and J. M. Grange. HIV/AIDS and its 18: 1–9, 1988.
implications for the control of animal tuberculosis.
[76] A. H. Cohen and R. M. Harris-Warrick. Strychnine Brit. Vet. J., 149: 405–417, 1993.
eliminates alternating motor output during fictive [95] J. C. Dallon and H. G. Othmer. A discrete cell locomotion in lamprey. Brain Res., 293: 164–167, model with adaptive signalling for aggregation of Phil. Trans. R. Soc. [77] A. H. Cohen, P. J. Holmes, and R. R. Rand. The Lond. B, 352: 391–417, 1997.
nature of coupling between segmental oscillators [96] P. DeBach. Biological Control by Natural Enemies.
and the lamprey spinal generator for locomotion: Cambridge University Press, Cambridge, 1974.
a mathematical model. J. Math. Biol., 13: 345– [97] R. J. DeBoer and A. S. Perelson.
toires and competitive exclusion. J. theor. Biol., [78] A. H. Cohen, S. Rossignol, and S. Grillner, edi- 169: 375–390, 1994.
tors. Neural Control of Rhythmic Movements in [98] O. Decroly and A. Goldbeter. From simple to com- Vertebrates. John Wiley, New York, 1988.
plex oscillatory behaviour: analysis of bursting in [79] A. H. Cohen and P. Wall´ en. The neuronal correlate a multiply regulated biochemical system. J. theor. of locomotion in fish. Exp. Brain Res., 41: 11–18, Biol., 124: 219–250, 1987.
[99] D. C. Deeming and M. W. J. Ferguson. Environ- [80] D. S. Cohen and J. D. Murray. A generalized dif- mental regulation of sex determination in reptiles.
fusion model for growth and dispersal in a popula- Phil. Trans. R. Soc. Lond. B, 322: 19–39, 1988.
tion. J. Math. Biol., 12: 237–249, 1981.
[100] D. C. Deeming and M. W. J. Ferguson. The mech- [81] J. E. R. Cohen and J. D. Murray. On nonlinear anism of temperature dependent sex determination convection dispersal effects in an interacting pop- in crocodilians: a hypothesis. Am. Zool., 29: 973– ulation model. SIAM J. Appl. Math., 43: 66–78, [101] D. C. Deeming and M. W. J. Ferguson. In the heat [82] Y. Cohen. Applications of Control Theory in Ecol- of the nest. New Scientist, 25: 33–38, 1989b.
ogy, volume 73 of Lect. Notes in Biomathe-mat- [102] D. Dellwo, H. B. Keller, B. J. Matkowsky, and E.
ics. Springer-Verlag, Berlin-Heidelberg-New York, L. Reiss. On the birth of isolas. SIAM J. Appl. Math., 42: 956–963, 1982.
[83] E. H. Colbert and M. Morales.
Evolution of [103] J. Demongeot and C. Jacob. Confineurs: une ap- the Vertebrates: A History of Backboned Animals proche stochastique. C. R. Acad. Sci., 56: 206– [121] E. C. Edblom and I. R. Epstein. A new iodate os- [104] J. Demongeot, P. M. Kulesa, and J. D. Murray.
cillator and Landolt reaction with ferrocyanide in Compact set valued flows: Applications in biolog- a CSTR. J. Amer. Chem. Soc., 108: 2826–2830, ical modelling. Acta Biotheoretica, 44: 349–358, [122] L. Edelstein-Keshet. Mathematical Models in Bi- [105] J. Demongeot, P. Pachot, P. Baconnier, G. Ben- ology. Random House, New York, 1988.
chetrit, S. Muzzin, and T. Pham Dinh. Entrain- [123] P. Ekman and W. V. Friesen. Facial Action Coding ment of the respiratory rhythm: concepts and tech- System. Consulting Psychologist Press, Palo Alto, niques of analysis. In G. Benchetrit, P. Baconnier, and J. Demongeot, editors, Concepts and Formal- [124] C. S. Elton. The Ecology of Invasions by Animals izations in the Control of Breathing, pages 217– and Plants. Methuen, London, 1958.
232. Manchester University Press, Manchester, [125] C. S. Elton and M. Nicholson. The ten-year cycle in numbers of lynx in Canada. J. Anim. Ecol., 191: [106] O. Diekman, J. A. P. Heesterbeek, and J. A. J.
215–244, 1942.
Metz. On the definition and the computation of [126] G. B. Ermentrout. n: m phase-locking of weakly the basic reproduction ratio R0 in models for in- coupled oscillators. J. Math. Biol., 12: 327–342, fectious diseases in heterogeneous populations. J. Math. Biol., 28: 365–382, 1990.
[127] G. B. Ermentrout.
An adaptive model for syn- [107] O. Diekmann and J. A. P. Heesterbeek. Mathemat- chrony in the firefly pteroptyx malaccae. J. Math. ical Epidemiology of Infectious Diseases: Model Biol., 29: 571–585, 1991.
Building, Analysis and Interpretation. John Wi- [128] P. Essunger and A. S. Perelson. Modeling HIV in- ley, New York, 2000.
fection of CD4+ T-cell subpopulations. J. theor. [108] D. C. Dietz and T. C. Hines. Alligator nesting in Biol., 170: 367–391, 1994.
North Central Florida. Copeia, 2: 249–258, 1980.
[129] L. Euler. A general investigation into the mortality [109] K. Dietz. The population dynamics of onchocersia- and multiplication of the human species. Theor. sis. In R. M. Anderson, editor, Population Dynam- Popl. Biol., 1: 307–314, 1970. (Reprinted from: ics of Infectious Diseases, pages 209–241. Chap- Euler, Leonhard. "Recherches g´ erales sur la mor- man and Hall, London, 1982.
e et la multiplication du genre humain," His- [110] K. Dietz and K. P. Hadeler. Epidemiological mod- toire de l' Acad´ emie Royale des Sciences et Belles els for sexually transmitted diseases.
Lettres, ann´ ee 1760, pp. 144–164, Berlin, 1767).
Biol., 26: 1–25, 1988.
[130] K. J. Falconer.
Fractal Geometry. Mathemati- [111] K. Dietz and D. Schenzle. Mathematical models cal foundations and Applications. John Wiley and for infectious disease statistics. In A Celebration of sons, Ithaca, New York, 1990.
Statistics: The ISI (International Statistics Insti- tute) Centenary Volume, pages 167–204. Springer- [131] E. V. Famiglietti. New metrics for analysis of den- Verlag, New York, 1985.
dritic branching patterns. Demonstrating similari- [112] C. A. Donnelly, N. M. Ferguson, A. C. Ghani, M.
ties in ON and ON-OFF directionally selective reti- E. J. Woolhouse, C. J. Watt, and R. M. Anderson.
nal gangliion cells. J. Compar. Neurol, 324: 295– The epidemiology of BSE in cattle herds in great britain. I Epidemiological processes, demography [132] M. J. Feigenbaum. Quantitative universality for a of cattle and approaches to control and culling.
class of nonlinear transformations. J. Stat. Phys., Phil. Trans. R. Soc. Lond. B, 352: 781–801, 1997.
19: 25–52, 1978.
[113] S. Douady and Y. Couder. Phyllotaxis as a physi- [133] M. W. J. Ferguson. Reproductive biology and em- cal self-organised growth process. Phys. Rev. Let- bryology of the crocodilians. In C. Gans, F. Billet, ters, 68: 2098–2101, 1992.
and P. Maderson, editors, Biology of the Reptilia, [114] S. Douady and Y. Couder. La physique des spirales volume 14A, pages 329–491. JohnWiley and Sons, etales. La Recherche, 24(250): 26–35, 1993a.
New York, 1985.
[115] S. Douady and Y. Couder. Phyllotaxis as a self- [134] M. W. J. Ferguson and T. Joanen. Temperature organised growth process. In J. M. Garcia-Ruiz et of egg-incubation determines sex in Alligator mis- al. , editors, Growth Patterns in Physical Sciences sissippiensis. Nature, 296: 850–853, 1982.
and Biology. Plenum Press, New York, 1993b.
[135] M. W. J. Ferguson and T. Joanen. Temperature- [116] R. D. Driver.
Ordinary and Delay Differen- dependent sex determination in Alligator missis- tial Equations. Springer-Verlag, Berlin-Heidelberg- sippiensis. J. Zool. Lond., 200: 143–177, 1983.
New York, 1977.
[136] N. M. Ferguson, C. A. Donnelly, M. E. J. Wool- [117] P. Duesberg. Inventing the AIDS Virus. Regnery house, and R. M. Anderson.
Press, Washington D. C. Lanham MD, 1996.
of BSE in cattle herds in great britain. II model [118] P. Duffy, J. Wolf, et al. Possible person-to-person construction and anlysis of transmission dynam- transmission of Creitzfeldt-Jakob disease. N. Engl. ics. Phil. Trans. R. Soc. Lond. B, 352: 803–838, J. Med., 290: 692–693, 1974.
[119] R. G. Duggleby.
Progress curves of reactions ere and M. Gatto. Chaotic population dy- catalyzed by unstable enzymes. A theoretical ap- namics can result from natural selection. Proc. R. proach. J. theor. Biol., 123: 67–80, 1986.
Soc. Lond. B, 251: 33–38, 1993.
[120] D. J. D. Earn, P. Rohani, and B. T. Grenfell. Per- [138] V. A. Ferro, J. E. O'Grady, J. Notman, and W.
sistence, chaos and synchrony in ecology and epi- H. Stimson. Development of a GnRH-neutralising demiology. Proc. R. Soc. Lond. B, 265: 7–10, 1998.
vaccine for use in hormone dependent disorders.
Therapeutic Immunol., 2: 147–157, 1995.
glion cell of the cat retina and its presynaptic cell [139] V. A. Ferro and W. H. Stimson.
types. J. Neurosci., 8: 2303–2320, 1988.
juvant, dose and carrier pre-sensitization on the [158] C. L. Frenzen and P. K. Maini. Enzyme kinetics efficacy of a GnRH analogue.
Drug Design and for a two-step enzymatic reaction with comparable Discovery, 14: 179–195, 1996.
initial enzyme-substrate ratios. J. Math. Biol., 26: [140] V. A. Ferro and W. H. Stimson. Fertility disrupt- 689–703, 1988.
ing potential of synthetic peptides derived from [159] R. R. Frerichs and J. Prawda. A computer simu- the beta subunit of follicles stimulating hormone.
lation model for the control of rabies in an urban Amer. J. Reprod. Immunol., 40: 187–197, 1998.
area of Colombia. Management Science, 22: 411– [141] R. J. Field and M. Burger, editors. Oscillations and Travelling Waves in Chemical Systems. John [160] S. D. W. Frost and A. R. McLean. Germinal center Wiley, New York, 1985.
destruction as a major pathway of HIV pathogen- [142] R. J. Field, E. K¨ os, and R. M. Noyes.
esis. J. AIDS, 7: 236–244, 1994.
cillations in chemical systems, Part 2. Thorough [161] N. Ganapathisubramanian and K. Showalter. Bi- analysis of temporal oscillations in the bromate- stability, mushrooms and isolas. J. Chem. Phys., cerium-malonic acid system. J. Am. Chem. Soc., 80: 4177–4184, 1984.
94: 8649–8664, 1972.
[162] C. Gans, F. Billet, and P. F. A. Maderson, editors.
[143] R. J. Field and R. M. Noyes. Oscillations in chem- Biology of the Reptilia, volume Volume 14A, De- ical systems, IV. limit cycle behaviour in a model velopment. John Wiley and Sons, New York, 1985.
of a real chemical reaction. J. Chem. Phys., 60: [163] L. Garrett. The Coming Plague: Newly Emerg- 1877–1884, 1974.
ing Diseases in a World Out of Balance. Penquin, [144] P. C. Fife. Mathematical aspects of reacting and U.S.A. , New York, 1994.
diffusing systems. In Lect. Notes in Biomathemat- [164] L. Garrett. The return of infectious disease. For- ics, volume 28. Springer-Verlag, Berlin-Heidelberg- eign Affairs, 75: 66–79, 1996.
New York, 1979.
ar and K. Showalter.
[145] P. C. Fife and J. B. McLeod.
for the oscillatory iodate oxidation of sulfite ferro- solutions of nonlinear diffusion equations to trav- cyanide. J. Physical Chem., 94: 4973–4979, 1990.
elling wave solutions. Archiv. Rat. Mech. Anal., [166] A. Georges. Female turtles from hot nests: is it du- 65: 335–361, 1977.
ration of incubation or proportion of development [146] F. D. Fincham, T. N. Bradbury, and C. K. Scott.
at high temperatures that matters? Oecologia, 81: Cognition in marriage. In F. D. Fincham and T.
323–328, 1989.
N. Bradbury, editors, The Psychology of Marriage, [167] A. Georges, C. Limpus, and R. Stoutjesdijk.
pages 118–149. Guildford, New York, 1990.
Hatchling sex in the marine turtle Caretta caretta [147] G. H. Fisher. Preparation of ambiguous stimulus is determined by proportion of development at a material. Perception and Psychophysics, 2: 421– temperature, not daily duration of exposure. J. Exp. Zool., 270: 432–444, 1994.
[148] R. A. Fisher. The wave of advance of advantageous [168] W. M. Getz and R. G. Haight. Population Har- genes. Ann. Eugenics, 7: 353–369, 1937.
vesting DemographicModels of Fish, Forest, and [149] R. A. Fisher. The Genetical Theory of Natural Se- Animal Resources. Princeton University Press, NJ, lection. Dover, New York, 1958. (Reprint of 1930 Princeton, NJ, 1989.
[169] A. Gierer and H. Meinhardt. A theory of biological [150] R. FitzHugh. Impulses and physiological states in pattern formation. Kybernetik, 12: 30–39, 1972.
theoretical models of nerve membrane. Biophys. [170] J. C. Gilkey, L. F. Jaffe, E. B. Ridgeway, and G.
J., 1: 445–466, 1961.
T. Reynolds. A free calcium wave traverses the ac- [151] J. C. Flores.
A mathematical model for nean- tivating egg of Oryzias latipes. J. Cell. Biol., 76: derthal extinction. J. theor. Biol., 191: 295–298, 448–466, 1978.
[171] M. E. Gilpin. Do hares eat lynx? Amer. Nat., 107: [152] K. R. Foster, M. E. Jenkins, and A. C. Toogood.
727–730, 1973.
The Philadelphia Yellow Fever Epidemic of 1793.
[172] L. Glass and M. C. Mackey. Pathological condi- Sci. Amer., pages 88–93, August 1998.
tions resulting from instabilities in physiological [153] B. J. Fowers and D. H. Olson. Predicting marital control systems. Ann. N. Y. Acad. Sci., 316: 214– success with prepare: a predictive validity study.
J. Marital and Family Therapy, 12: 403–413, 1986.
[173] L. Glass and M. C. Mackey. From Clocks to Chaos: [154] A. C. Fowler. Mathematical Models in the Applied The Rhythms of Life. Princeton University Press, Sciences. Cambridge University Press, Cambridge, NJ, Princeton, 1988.
[174] R. W. Glenny, S. McKinney, and H. T. Robert- [155] A. C. Fowler and G. P. Kalamangalam. The role son. Spatial pattern of pulmonary blood flow dis- of the central chemoreceptor in causing periodic tribution is stable over days. J. Appl. Physiol., 82: breathing. IMA J. Math. Appl. Medic. and Biol., 902–907, 1997.
17: 147–167, 2000.
[175] R. W. Glenny, N. L. Polissar, S. McKinney, and [156] J. P. Fox, I. Elveback, W. Scott, L. Gatewood, and H. T. Robertson. Temporal heterogeneity of re- E. Ackerman. Herd immunity: basic concept and gional pulmonary perfusion is spatially clustered.
relevance to public health immunization practice.
J. Appl. Physiol., 79: 986–1001, 1995.
Am. J. of Epidemiology, 94: 179–189, 1971.
[176] R. W. Glenny and H. T. Robertson. Fractal prop- [157] M. A. Freed and P. Sterling. The ON-alpha gan- erties of pulmonary blood flow: characterization of spatial heterogeneity. J. Appl. Physiol., 69: 532– The mathematics of marital conflict: namic mathematical nonlinear modeling of new- [177] R. W. Glenny and H. T. Robertson. Applications lywed marital interaction. J. Family Psychol., 13: of fractal analysis to physiology. J. Appl. Physiol., 1–17, 1999.
70: 2351–2367, 1991.
[194] P. Gray. Instabilities and oscillations in chemical [178] R. W. Glenny and H. T. Robertson. Fractal mod- reactions in closed and open systems. Proc. R. Soc. eling of pulmonary blood flow heterogeneity.
Lond. A, 415: 1–34, 1988.
Appl. Physiol., 70: 1024–1030, 1991.
[195] P. Gray and S. K. Scott. Autocatalytic reactions [179] R. W. Glenny and H. T. Robertson. A computer in the isothermal continuous stirred tank reactor.
simulation of pulmonary perfusion in three dimen- Chem. Eng. Sci., 38: 29–43, 1983.
sions. J. Appl. Physiol., 79: 357–369, 1995.
[196] P. Gray and S. K. Scott. A new model for oscilla- [180] B.-S. Goh. Management and Analysis of Biolog- tory behaviour in closed systems: the autocatala- ical Populations. Elsevier Sci. Pub., Amsterdam, tor. Ber. Bunsenges. Phys. Chem., 90: 985–996, [181] A. Goldbeter. Models for oscillations and excitabil- [197] J. S. Griffith. Mathematics of cellular control pro- ity in biochemical systems.
In L. A. Segel, edi- cesses. I. Negative feedback to one gene. II. Positive tor, Mathematical Models in Molecular and Cellu- feedback to one gene. J. theor. Biol., 20: 202–216, lar Biology, pages 248–291. Cambridge University Press, Cambridge, 1980.
[198] S. Grillner.
On the generation of locomotion in the spinal dogfish. Exp. Brain Res., 20: 459–470, and Cel-lular of periodic and chaotic behaviour.
[199] S. Grillner and S. Kashin. On the generation and University Press, Cambridge, 1996.
performance of swimming fish. In R. M. Herman, [183] S. Goldstein and J. D. Murray.
S. Grillner, P. S. G. Stein, and D. G. Stuart, ed- matics of exchange processes in fixed columns. III.
itors, Neural Control of Locomotion, pages 181– The solution for general entry conditions, and a 202. Plenum, New York, 1976.
method of obtaining asymptotic expressions. IV.
[200] S. Grillner and P. Wall´ en. On the peripheral con- Limiting values, and correction terms, for the trol mechanisms acting on the central pattern gen- kinetic-theory solution with general entry condi- erators for swimming in dogfish. J. Exp. Biol., 98: tions. V. The equilibrium-theory and perturbation 1–22, 1982.
solutions, and their connection with kinetic-theory [201] P. Grindrod.
The Theory and Applications solutions, for general entry conditions. Proc. R. of Reaction-Diffusion Equations? Patterns and Soc. Lond. A, 257: 334–375, 1959.
Waves. Oxford University Press, New York, 1996.
[184] B. C. Goodwin.
Oscillatory behaviour in enzy- [202] G. Gros, D. Lavalette, W. Moll, H. Gros, B.
matic control processes.
Adv. in Enzyme Regu- Amand, and F. Pichon. Evidence of rotational con- lation, 3: 425–438, 1965.
tribution to protein-facilitated proton transport.
[185] T. M. Goodwin and W. R. Marion. Aspects of the Proc. Natl. Acad. Sci. U.S.A., 81: nesting ecology of American alligators (Alligator mississippiensis) in North Central Florida. Her- [203] G. Gros, W. Moll, H. Hoppe, and H. Gros. Pro- petologica, 34: 43–47, 1978.
ton transport by phosphase diffusion-a mechnism [186] J. M. Gottman. Marital Interaction: Experimental of facilitated CO2 transfer. J. Gen. Physiol., 67: Investigations. Academic Press, New York, 1979.
773–790, 1976.
[187] J. M. Gottman. How marriages change. In G. R.
[204] J. Guckenheimer and P. J. Holmes. Nonlinear Os- Patterson, editor, Advances in Family Research. cillations, Dynamical Systems and Bifurcations of Depression and Aggression in Family Interaction, Vector Fields. Springer-Verlag, Berlin-Heidelberg- pages 75–101. Lawrence Erlbaum, Hillsdale, NJ, New York, 1983.
[205] M. R. Guevara and L. Glass.
[188] J. M. Gottman. The roles of conflict engagement, period-doubling bifurcations and chaos in a math- escalation, or avoidance in marital interaction: A ematical of a periodically driven biological oscil- longitudinal view of five types of couples. J. Con- lator: A theory for the entrainment of biological sulting and Clinical Psychol., 61: 6–15, 1993.
oscillators and the generation of cardiac dysrhyth- [189] J. M. Gottman. What Predicts Divorce? Lawrence mias. J. Math. Biol., 14: 1–23, 1982.
Erlbaum, Hillsdale, NJ, 1994.
[206] M. R. Guevara, L. Glass, and A. Shrier. Phase- [190] J. M. Gottman. Psychology and the study of mar- locking, period-doubling bifurcations and irregular ital processes. Annu. Rev. Psychol., 49: 169–197, dynamics in periodically stimulated cardiac cells.
Science, 214: 1350–1353, 1981.
[191] J. M. Gottman and R. W. Levenson.
[207] I. Gumowski and C. Mira. Dynamique Chaotique.
processes predictive of later dissolution: behavior, Collection Nabla. Cepadue, Toulouse, 1980.
psychology, and health. J. Personality and Social [208] G. H. Gunaratne, Q. Ouyang, and H. L. Swinney.
Psychol., 63: 221–233, 1992.
Pattern formation in the presence of symmetries.
[192] J. M. Gottman, J. D. Murray, C. Swanson, R. C.
Phys. Rev. E, 50: 2802–2820, 1994.
Tyson, and K. R. Swanson. The Mathematics of [209] W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet.
Marriage: Dynamic Nonlinear Models. MIT Press, Nicholson's blowflies revisited. Nature, 287: 17–21, Cambridge, MA, 2002.
[193] J. M. Gottman, C. B. Swanson, and J. D. Mur- [210] W. S. C. Gurney and R. M. Nisbet.
density-dependent population dynamics in static [229] H. W. Hethcote, H. W. Stech, and P. van den and variable environments. Theor. Popul. Biol., Driessche. Nonlinear oscillations in epidemic mod- 17: 321–344, 1980.
els. SIAM J. Appl. Math., 40: 1–9, 1981.
[211] M. E. Gurtin and R. C. MacCamy. Non-linear age- [230] H. W. Hethcote and J. A. Yorke. Gonorrhea trans- dependent population dynamics. Arch. Rat. Mech. mission dynamics and control. In Lect. Notes in Anal., 54: 281–300, 1974.
Biomathematics, volume 56. Springer-Verlag, Hei- [212] R. Guttman, S. Lewis, and J. Rinzel.
delberg, 1984.
of repetitive firing in squid axon membrane as a [231] H. W. Hethcote, J. A. Yorke, and A. Nold. Gonor- model for a neurone oscillator. J. Physiol. (Lond.), rhea modelling: a comparison of control methods.
305: 377–95, 1980.
Math. Biosci., 58: 93–109, 1982.
[213] W. H. N. Gutzke and D. Crews. Embryonic tem- [232] R. Hilborn and M Mangel.
The Ecological De- perature determines adult sexuality in a reptile.
tective. Confronting models with data. Princeton Nature, 332: 832–834, 1988.
University Press, NJ, Princeton, NJ, 1997.
orgyi and R. J. Field. Simple models of de- [233] D. D. Ho, A. U. Neumann, A. S. Perelson, W.
terministic chaos in the Belousov-Zhabotinsky re- Chen, J. M. Leonard, and M. Markowitz. Rapid action. J. Chem. Phys., 95: 6594–6602, 1991.
turnover of plasma virions and CD4 lymphocytes [215] P. A. Hall and D. A. Levinson.
in HIV-1 infection. Nature, 373: 123–126, 1995.
cell proliferation in histological material. J. Clin. [234] A. L. Hodgkin and A. F. Huxley. A quantitative de- Pathology, 43: 184–192, 1990.
scription of membrane current and its application [216] M. Hancox. The great badgers and bovine TB de- to conduction and excitation in nerve. J. Physiol. bate. Biologist, 42: 159–161, 1995.
(Lond.), 117: 500–544, 1952.
[217] F. E. Hanson. Comparative studies of firefly pace- [235] A. V. Holden, editor. Chaos. Manchester Univer- makers. Federation Proceedings, 37(8): 2158–2164, sity Press, Manchester, 1986.
[236] E. Hooper.
The River: A Journey Back to the [218] P. Hanusse. De l'´ existence d'un cycle limit dans Source of HIV and AIDS. Little Brown and Co., evolution des syst emes chimique ouverts (on the Waltham, MA, U.S.A. , 1999.
existence of a limit cycle in the evolution of open [237] L. Hopf. Introduction to Differential Equations of chemical systems). Comptes Rendus, Acad. Sci. Physics. Dover, New York, 1948.
Paris, (C), 274: 1245–1247, 1972.
[238] F. C. Hoppensteadt.
Mathematical Theories of [219] D. C. Hassell, D. J. Allwright, and A. C. Fowler.
Demographics, Genetics and Epi- A mathematical analysis of Jones' site model for demics, volume 20 of CBMS Lectures. SIAM Pub- spruce budworm infestations. J. Math. Biol., 38: lications, Philadelphia, 1975.
377–421, 1999.
[239] F. C. Hoppensteadt.
Mathematical Methods in Population Biology. Cambridge University Press, pod Predator-Prey Systems. Princeton University Cambridge, 1982.
Press, NJ, Princeton, 1978.
[240] F. Hoppensteadt. An Introduction to the Math- [221] M. P. Hassell, R. M. May, and J. Lawton. Pattern ematics of Neurons. Cambridge University Press, of dynamic behaviour in single species populations.
Cambridge, 1985.
J. Anim. Ecol., 45: 471–486, 1976.
[241] F. C. Hoppensteadt and J. M. Hyman. Periodic [222] A. Hastings.
Population Biology (1st edition solutions to a discrete logistic equation. SIAM J. 1997). New York, Springer-Verlag, 2000.
Appl. Math., 32: 985–992, 1977.
[223] S. P. Hastings and J. D. Murray. The existence [242] F. C. Hoppensteadt and J. D. Murray. Thresh- of oscillatory solutions in the Field-Noyes model old analysis of a drug use epidemic model. Math. for the Belousov-Zhabotinskii reaction. SIAM J. Biosci., 53: 79–87, 1981.
Appl. Math., 28: 678–688, 1975.
[243] F. C. Hoppensteadt and C. S. Peskin. Mathemat- [224] S. P. Hastings, J. J. Tyson, and D. Webster. Ex- ics in Medicine and the Life Sciences. Springer- istence of periodic solutions for negative feedback Verlag, Berlin-Heidelberg-New York, 1992.
control systems. J. Differential Eqns., 25: 39–64, [244] Y. Hosono. Travelling wave solutions for some den- sity dependent diffusion equations. Japan J. Appl. [225] W. J. Herbert, P. C. Wilkinson, and D. I. Stott.
Math., 3: 163–196, 1986.
Life, Death and the Immune System. W. H. Free- [245] Y. Hosono. Travelling wave for some biological sys- man, New York, 1994.
tems with density dependent diffusion. Japan J. [226] V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M.
Appl. Math., 4: 297–359, 1987.
May, and M. A. Nowak. Viral dynamics in vivo: [246] L. N. Howard. Nonlinear oscillations. Amer. Math. Limitations on estimations on intracellular delay Soc. Lect. Notes in Appl. Math., 17: 1–67, 1979.
and virus decay. Proc. Nat. Acad. Sci. USA, 93: [247] L. N. Howard and N. Kopell. Slowly varying waves 7247–7251, 1996.
and shock structures in reaction-diffusion equa- [227] H. W. Hethcote. Measles and rubella in the united tions. Studies in Appl. Math., 56: 95–145, 1977.
states, qualitative analysis of communicable dis- [248] A. H. Howe. A Theoretical Inquiry into the Phys- ease models.
Am. J. Epidemiology, 117: 2–13, ical Cause of Epidemic Diseases. J. Churchill and Son, London, 1865.
[228] H. W. Hethcote.
Three basic epidemiologi- [249] S-B. Hsu, S. P. Hubbell, and P. Waltman. A contri- cal models. In S. A. Levin, editor, Lect. Notes bution to the theory of competing predators. Eco- in Biomathematics, volume 100, pages 119–144.
logical Monographs, 48: 337–349, 1979.
Springer-Verlag, Heidelberg, 1994.
[250] B. A. Huberman. Striations in chemical reactions.
J. Chem. Phys., 65: 2013–2019, 1976.
coral morphology. Physical Rev. Lett., 77: 2328– [251] C. Huffaker, editor.
Biological Control. Plenum Press, New York, 1971.
[271] R. R. Kao, M. G. Roberts, and T. J. Ryan.
[252] A. Hunding. Limit-cycles in enzyme systems with model of bovine tuberculosis control in domesti- nonlinear feedback. Biophys. Struct. Mech., 1: 47– cated cattle herds. Proc. R. Soc. Lond. B, 264: 1069–1076, 1997.
[253] L. D. Iasemidis and J. C. Sackellares. Chaos the- [272] P. M. Kareiva.
Local movement in herbivo- ory and epilepsy. The Neuroscientist, 2: 118–126, rous insects: applying a passive diffusion model to markrecapture field experiments.
[254] V. Isham. Mathematical modelling of the trans- (Berlin), 57: 322–327, 1983.
mission dynamics of HIV infection and AIDS: a [273] W. L. Kath and J. D. Murray. Analysis of a model review. J. Roy. Stat. Soc. A, 151: 5–30, 1988.
biological switch. SIAM J. Appl. Math., 45: 943– [255] IWC. Report no. 29. Technical report, Interna- tional Whaling Commission, Cambridge, 1979.
[274] M. J. Keeling and C. A. Gilligan. Bubonic plague: ager and S. Luckhaus. On explosion of solu- a metapopulation model of a zoonosis. Proc. R. tions to a system of partial differential equations Soc. B, 267: 2219–2230, 2000.
modelling chemotaxis. Trans. Amer. Math. Soc., [275] J. Keener and L. Glass. Global bifurcations of a 329: 819–824, 1992.
periodically forced nonlinear oscillator. J. Math. [257] J. Jalife and C. Antzelevitch. Phase resetting and Biol., 21: 175–190, 1984.
annihilation of pacemaker activity in cardiac tis- [276] J. Keener and J. Sneyd. Mathematical Physiology.
sue. Science, 206: 695–697, 1979.
Springer, New York, 1998.
[258] W. H. James. Re: Total serum testosterone and gonadotrophins in workers exposed to dioxin. Am. [277] E. F. Keller and L. A. Segel. Initiation of slime J. Epidemiol., 141: 476–477, 1995.
mold aggregation viewed as an instability. J. theor. [259] W. H. James. Evidence that mammalian sex ra- Biol., 26: 399–415, 1970.
tios at birth are partially controlled by parental [278] E. F. Keller and L. A. Segel.
hormone levels at the time of conception. J. theor. of chemotactic bacteria: a theoretical analysis. J. Biol., 180: 271–286, 1996.
theor. Biol., 30: 235–248, 1971.
[260] W. H. James. Further evidence relating offspring [279] W. O. Kermack and A. G. McKendrick. Contri- sex ratios to parental hormone levels around the butions to the mathematical theory of epidemics.
time of conception. J. theor. Biol., 197: 261–263, Proc. R. Soc. Lond. A, 115: 700–721, 1927.
[280] W. O. Kermack and A. G. McKendrick. Contri- [261] W. H. James. The hypothesized hormonal control butions to the mathematical theory of epidemics.
of offspring sex ratio: evidence from families as- Proc. R. Soc. Lond. A, 138: 55–83, 1932.
certained by schizophrenia and epilepsy. J. theor. [281] W. O. Kermack and A. G. McKendrick. Contri- Biol., 206: 445–447, 2000.
butions to the mathematical theory of epidemics.
[262] T. Joanen.
Nesting ecology of alligators in Proc. R. Soc. Lond. A, 141: 94–122, 1933.
Louisiana. Proc. Ann. Conf. S. E. Assoc. Game [282] J. Kevorkian.
Partial Differential Equations: and Fish Comm., 23: 141–151, 1969.
[263] T. Joanen and L. McNease. A telemetric study Springer-Verlag, New York, 2000.
of nesting female alligators on Rockefeller Refuge, [283] J. Kevorkian and J. D. Cole. Multiple Scale and Louisiana. Proc. Ann. Conf. S. E. Assoc. Game Singular Perturbation Methods. Springer-Verlag, and Fish Comm., 24: 175–193, 1970.
New York, 1996.
[264] T. Joanen and L. McNease. Notes on the reproduc- [284] N. Keyfitz.
Introduction to the Mathematics of tive biology and captive propagation of the Ameri- Population. Addison-Wesley, Reading, MA, 1968.
can alligator. Proc. Ann. Conf. S. E. Assoc. Game [285] S. Kingsland.
Modeling Nature: episodes in and Fish Comm., 25: 407–414, 1971.
the History of Population Ecology. University of [265] T. Joanen and L. McNease.
A telemetric stud- Chicago Press, Chicago, 1995.
y of adult male alligators on Rockefeller Refuge, [286] D. E. Kirschner and G. F. Webb. Understanding Louisiana. Proc. Ann. Conf. S. E. Assoc. Game drug resistance for monotherapy treatment of HIV and Fish Comm., 26: 252–275, 1972.
infection. Bull. Math. Biol., 59: 763–785, 1997.
[266] S. D. Johnson. Sex ratio and population stability.
[287] A. Kolmogoroff, I. Petrovsky, and N. Piscounoff.
Oikos, 69: 172–176, 1994.
equation de la diffusion avec croissance [267] C. M. Johnston, M. Barnett, and P. T. Sharpe.
ere et son application The molecular biology of temperature-dependent eme biologique. Moscow University, Bulletin sex determination. Phil. Trans. R. Soc. Lond. B, Math., 1: 1–25, 1937.
350: 297–304, 1995.
[288] N. Kopell. Toward a theory of modelling central [268] D. W. Jordan and P. Smith. Nonlinear Ordinary pattern generators.
In A. H. Cohen, S. Rossig- Differential Equations. Oxford University Press, nol, and S. Grillner, editors, Neural Control of Oxford, third edition, 1999.
Rhythmic Movements in Vertebrates, pages 369– [269] J. Kaandorp, editor.
Fractal Modelling. Growth 414. John Wiley, New York, 1988.
and Form in Biology. Springer-Verlag, Heidelberg, [289] N. Kopell and L. N. Howard. Horizontal bands in the Belousov reaction. Science, 180: 1171–1173, [270] J. K. Kaandorp, C. P. Lowe, D. Frenkel, and P. M.
A. Sloot. Effect of nutrient diffusion and flow on [290] T. Kostova. Numerical solutions to equations mod- [309] E. Leigh. The ecological role of Volterra's equa- elling nonlinearly interacting age-dependent pop tions. In M. Gerstenhaber, editor, Some mathe- Comput. Math. appl., 19(8): matical problems in biology, pages 1–64.
Math. Soc., Providence, 1968.
[291] M. Kot. Discrete-time travelling waves: ecological [310] P. H. Leslie.
On the use of matrices in certain examples. J. Math. Biol., 30: 413–436, 1992.
population mathematics. Biometrika, 33: 183–212, [292] M. Kot. Elements of Mathematical Ecology. Cam- bridge University Press, Cambridge, UK, 2001.
[311] P. H. Leslie. Some further notes on the use of ma- [293] M. Kot, M. Lewis, and P. van den Driessche. Dis- trices in population mathematics. Biometrika, 35: persal data and the spread of invading organisms.
213–245, 1945.
Ecology, 77: 2027–2042, 1996.
[312] S. A. Levin, editor. Frontiers in Mathematical Bi- [294] V. I. Krinsky. Mathematical models of cardiac ar- ology, volume 100 of Lect. Notes in Biomathemat- rhythmias (spiral waves). Pharmac. Ther. (B), 3: ics. Springer-Verlag, Berlin-Heidelberg-New York, 539–555, 1978.
[295] L. J. Krokoff, J. M. Gottman, and S. D. Haas. Val- [313] E. R. Lewis. Network Models in Population Biol- idation of rapid couples interaction scoring system.
ogy. Springer-Verlag, Berlin-Heidelberg-New York, Behavioral Assessment, 11: 65–79, 1989.
[296] H. Kruuk. Spatial organization and territorial be- [314] M. A. Lewis. Variability, patchiness, and jump dis- haviour of the european badger Meles meles. J. persal in the spread of an invading population. In Zool. Lond., 184: 1–19, 1978.
D. Tilman and P. Kareiva, editors, Spatial Ecology. [297] M. Kunz and F. Rothen. Phyllotaxis or the prop- The Role of Space in Population Dynamics and erties of spiral lattices. III. An algebraic model of Interspecific Interactions, pages 46–69. Princeton J. Phys. Inst. France, 2: 2131– University Press, NJ, Princeton, NJ, 1997.
[315] M. A. Lewis and G. Schmitz. Biological invasion of [298] K. J. Laidler and P. S. Bunting.
The Chemical an organism with separate mobile and stationary Kinetics of Enzyme Action. Clarendon Press, Ox- states: modeling and anlaysis. Forma, 11: 1–25, [299] A. Lajmanovich and J. A. Yorke. A deterministic [316] T.-Y. Li, M. Misiurewicz, G. Pianigiani, and J. A.
model for gonorrhea in a nonhomogeneous popu- Yorke. Odd chaos. Phys. Letters(A), 87: 271–273, lation. Math. Biosci., 28: 221–236, 1976.
[300] D. C. Lane, J. D. Murray, and V. S. Manoran- [317] T.-Y. Li and J. A. Yorke.
Period three implies Analysis of wave phenomena in a morpho- chaos. Amer. Math. Monthly, 82: 985–992, 1975.
genetic mechanochemical model and an applica- [318] L. S. Liebovitch. Fractals and Chaos Simplified for tion to post-fertilisation waves on eggs. IMA J. the Life Sciences. Oxford University Press, Ox- Math. Applied in Medic. and. Biol., 4: 309–331, [319] L. A. Lipsitz and A. L. Goldberger. Loss of ‘com- [301] J. W. Lang. Crocodilian thermal selection. In G.
plexity' and aging. Potential applications of frac- J. W. Webb, S. C. Manolis, and P. J. Whitehead, tals and chaos theory to senescence. JAMA, 267: editors, Wildlife Management: Crocodiles and Al- 1806–1809, 1992.
ligators, pages 301–317.
Surrey Beatty, Sydney, [320] E. N. Lorenz. Deterministic nonperiodic flow. J. Atmos. Sci., 20: 131–141, 1963.
[302] J. W. Lang and H. V. Andrews.
[321] A. J. Lotka. Studies on the mode of growth of ma- dependent sex determination in crocodilians.
terial aggregates. Am. J. Sci., 24: 199–216, 1907a.
Exp. Biol., 270: 28–44, 1994.
[322] A. J. Lotka.
Relation between birth and death [303] F. Lara-Ochoa.
A generalized reaction diffusion rates. Science, 26: 21–22, 1907b.
model for spatial structure formed by mobile cells.
[323] A. J. Lotka. Contribution to the theory of periodic Biosystems, 17: 35–50, 1984.
reactions. J. Phys. Chem., 14: 271–274, 1910.
[304] D. A. Larson. Transient bounds and time asymp- [324] A. J. Lotka. Vital statistics-a natural population totic behaviour of solutions of nonlinear equations norm. J. Wash. Ac. Sci., 3: 289–293, 1913.
of Fisher type. SIAM J. Appl. Math., 34: 93–103, [325] A. J. Lotka. Undamped oscillations derived from the law of mass action. J. Amer. Chem. Soc., 42: [305] R. Larter, B. Speelman, and R. M. Worth. A cou- 1595–1599, 1920.
pled ordinary differential equation lattice model for [326] A. J. Lotka.
Elements of Physical Biology.
the simulation of epileptic seizures. Chaos, 9: 795– Williams and Wilkins, Baltimore, 1925.
[327] J. A. Lubina and S. A. Levin. The spread of a rein- [306] D. A. Lauffenburger and K. H. Keller. Effects of vading species: range expansion in the California leukocyte random motility and chemotaxis in tis- sea otter. Amer. Naturalist, 131: 526–543, 1988.
sue inflammatory response.
J. theor. Biol., 81: [328] S. R. Lubkin, R. G. Gullberg, B. K. Logan, P. K.
475–503, 1979.
Maini, and J. D. Murray. Simple vs. sophisticated [307] J. Lauritsen.
The AIDS War: models for breath alcohol exhilation profiles. Alco- and genocide from the medical-industrial complex.
hol and Alcohohlism, 31: 61–67, 1996.
Asklepios, New York, 1993.
[329] D. Ludwig. Forest management strategies that ac- [308] H. Lauwerier. Two-dimensional iterative maps. In count for short-term and long-term consequences.
A. V. Holden, editor, Chaos, pages 58–95. Manch- Can. J. Forest Res., 23: 563, 1993.
ester University Press, Manchester, 1986.
[330] D. Ludwig.
Missed opportunities in natural re- source management. Natural Resource Modeling, interacting oscillatory systems. Biophys. Chem., 8(2): 111–117, 1994.
4: 241–248, 1975.
[331] D. Ludwig.
Uncertainty and fisheries manage- [351] J.-L. Martiel and A. Goldbeter. A model based on ment. In Frontiers in Mathematical Biology, vol- receptor desensitization for cyclic-AMP signalling ume 100 of Lect. Notes in Biomathematics, pages in Dictyostelium cells. Biophys. J., 52: 807–828, 516–528. Springer-Verlag, Berlin-Heidelberg-New [352] J. Clerk Maxwell. Scientific Papers. Dover, New [332] D. Ludwig.
A theory of sustainable harvesting.
SIAM J. Appl. Math., 55(2): 564–575, 1995.
[353] R. M. May.
Stability and Complexity in Model [333] D. Ludwig. Uncertainty and the determination of Ecosystems. Princeton Univ. Press, Princeton, sec- ond edition, 1975.
6(4): 1067–1076, 1996a.
[354] R. M. May. Theoretical Ecology. Principles and [334] D. Ludwig. The distribution of population survival Blackwell Scientific Publications, times. Amer. Naturalist, 147(4): 506–526, 1996b.
Oxford, second edition, 1981.
[335] D. Ludwig, R. Hillborn, and C. J. Walters. Un- [355] R. M. May. Regulation of population with nonover- certainty, resource exploitation and conservation: lapping generations by microparasites: a purely lessons from history. Science, 260: 17, 36, 1993.
chaotic system. Amer. Nat., 125: 573–584, 1985.
[336] D. Ludwig, D. D. Jones, and C. S. Holling. Qual- [356] R. M. May. When two and two do not make four: itative analysis of insect outbreak systems: the nonlinear phenomena in ecology.
Proc. R. Soc. spruce budworm and forest. J. Anim. Ecol., 47: Lond. B, 228: 241–266, 1986.
315–332, 1978.
[357] D. McFadden and E. G. Pasanen. Comparison of [337] D. Ludwig and C. Holling.
Sustainability, sta- the auditory systems of heterosexuals and homo- bility and resilience.
Conservation Ecol. [on- sexuals: click-evoked otoacoustic emissions. Proc. line], 1(7), 1997.
Natl. Acad. Sci. USA, 95: 2709–2713, 1998.
[358] H. P. McKean. Nagumo's equation. Adv. in Math., [338] R.-L. Luther. Rauemliche Fortpflanzung Chemis- 4: 209–223, 1970.
cher Reaktionen. Z. f¨ ur Elektrochemie und angew. [359] H. P. McKean. Application of Brownian motion to physikalische Chemie., 12(32): 506–600, 1906. En- the equation of Kolmogorov-Petrovskii-Piskunov.
glish translation: Arnold, R. and Showalter, K.
Comm. Pure Appl. Math., 28: 323–331, 1975.
and Tyson, J. J. In: Propagation of chemical reac- [360] A. G. McKendrick. Application of mathematics to tions in space, J. Chem. Educ. 64: 740–742, 1987.
medical problems. Proc. Ed. Math. Soc., 44: 98– [339] D. MacDonald. Badgers and bovine tuberculosis- case not proven. New Scientist, 104: 17–20, 1984.
[361] A. R. McLean and C. R. Mitchie. In vivo estimates [340] N. MacDonald.
Bifurcation theory applied to a of division and death rate of human lymphocytes.
simple model of a biochemical oscillator. J. theor. Proc. Nat. Acad. Sci. U. S. A., 92: 3707–3711, Biol., 65: 727–734, 1977.
[341] N. MacDonald.
Time lags in biological mod- [362] A. R. McLean and M. A. Nowak. Models of in- els. In Lecture Notes in Biomathematics, volume teractions between HIV and other pathogens. J. 28. Springer-Verlag, Berlin-Heidelberg-New York, theor. Biol., 155: 69–86, 1992.
[363] M. McNeill. Plagues and People. Anchor Books, [342] M. C. Mackey and L. Glass.
New York, 1989.
chaos in physiological control systems.
[364] J. A. J. Metz and O. Diekmann. The dynamics 197: 287–289, 1977.
of physiologically structured populations. In Lect. [343] M. C. Mackey and J. G. Milton. Dynamical dis- Notes in Biomathematics, volume 68.
eases. Ann. N. Y. Acad. Sci., 504: 16–32, 1988.
Verlag, Berlin-Heidelberg-New York, 1986.
[344] M. C. Mackey and J. G. Milton. Feedback delays [365] W. D. Metzen. Nesting ecology of alligators on the and the origins of blood cell dynamics. Comments Okefenokee National Wildlife Refuge. Proc. Ann. on modern biology. Part C. Comments on Theor. Conf. S. E. Assoc. Fish and Wildl. Agencies, 31: Biol., 1: 299–327, 1990.
29–32, 1977.
[345] MAFF. Bovine TB in badgers 1972–85. Scientific [366] E. R. Meyer. Crocodilians as Living Fossils. In N.
report, Ministry of Agric. Fish. and Food (Lon- Eldridge and M. Stanley, editors, Living Fossils, pages 105–131. Springer-Verlag, New York, 1984.
[346] MAFF. Bovine TB in badgers. Scientific report, [367] L. Michaelis and M. I. Menten. Die Kinetik der Ministry of Agric. Fish. and Food (London), 1994.
Invertinwirkung. Biochem. Z., 49: 333–369, 1913.
[347] T. R. Malthus. An essay on the Principal of Popu- [368] J. G. Milton and M. C. Mackey. Periodic haema- lation. Penguin Books, 1970. Originally published tological diseases: Mystical entities or dynamical J. Roy. Coll. of Physicians, 23: 236– [348] B. B. Mandelbrot. The Fractal Geometry of Na- ture. Freeman, San Francisco, 1982.
[369] R. E. Mirollo and S. H. Strogatz.
tion of pulse-coupled biological oscillators. SIAM [349] V. S. Manoranjan and A. R. Mitchell. A numerical J. Appl. Math., 50: 1645–1662, 1990.
study of the Belousov-Zhabotinskii reaction using [370] P. J. Mitchell and J. D. Murray. Facilitated dif- Galerkin finite element methods. J. Math. Biol., fusion: the problem of boundary conditions. Bio- 16: 251–260, 1983.
physik, 9: 177–190, 1973.
[350] M. Marek and I. Stuchl. Synchronization in two [371] J. E. Mittler, M. Markowitz, D. D. Ho, and A. S.
Perelson. Refined estimates for HIV-1 clearance Models in Biology. Clarendon Press, Oxford, 1977.
rate and intracellular delay. AIDS, 13: 1415–1417, [392] J. D. Murray. On pattern formation mechanisms for Lepidopteran wing patterns and mammalian [372] J. E. Mittler, B. Sulzer, A. U. Neumann, and A. S.
coat markings. Phil. Trans. R. Soc. Lond. B, 295: Perelson. Influence of delayed virus production on 473–496, 1981.
viral dynamics in HIV-1 infected patients. Math. [393] J. D. Murray. Parameter space for Turing instabil- Biosci., 152: 143–163, 1998.
ity in reaction diffusion mechanisms: a comparison [373] R. M. Miura.
Explicit roots of the cubic poly- of models. J. theor. Biol., 98: 143–163, 1982.
nomial and applications.
Appl. Math. Notes, 4: [394] J. D. Murray.
22–40, 1980.
Verlag, Berlin-Heidelberg-New York, second edi- [374] P. Moccarelli, P. Brambilla, P. M. Gerthoux, D.
G. Patterson, and L. L. Needham. Change in sex [395] J. D. Murray.
Use and abuse of fractal theory ratio with exposure to dioxin. Lancet, 348: 409, in neuroscience. J. Comp. Neurol., 361: 369–371, [375] G. Moda, C. J. Daborn, J. M. Grange, and O.
[396] J. D. Murray, J. Cook, S. R. Lubkin, and R. C.
Cosivi. The zoonic importance of Mycobacterium Spatial pattern formation in biology: I.
bovis. Tubercle Lung Disease, 77: 103–108, 1996.
dermal wound healing II. bacterial patterns.
[376] A. Mogilner and L. Edelstein-Keshet. A non-local Franklin Inst., 335: 303–332, 1998.
model for a swarm. J. Math. Biol., 38: 534–570, [397] J. D. Murray, D. C. Deeming, and M. W. J. Fer- guson. Size-dependent pigmentation-pattern for- [377] D. Mollison. Spatial contact models for ecological mation in embryos of Alligator mississippiensis: and epidemic spread. J. Roy. Stat. Soc.(B), 39: time of initiation of pattern generation mechanism.
283–326, 1977.
Proc. R. Soc. Lond. B, 239: 279–293, 1990.
[378] D. Mollison. Dependence of epidemic and popula- [398] J. D. Murray and C. L. Frenzen. A cell justification tion velocities on basic parameters. Math. Biosci., for Gompertz' equation. SIAM J. Appl. Math., 46: 107: 255–287, 1991.
614–629, 1986.
[379] A. Monk and H. G. Othmer. Cyclic AMP oscilla- [399] J. D. Murray, E. A. Stanley, and D. L. Brown. On tions in suspensions of Dictyostelium discoideum.
the spatial spread of rabies among foxes. Proc. R. Phil. Trans. R. Soc. Lond. B, 323: 185–224, 1989.
Soc. Lond. B, 229: 111–150, 1986.
[380] J. Monod and F. Jacob. General conclusions: teleo- [400] J. D. Murray and G. F. Oster. Cell traction models nomic mechanisms in cellular metabolism, growth for generating pattern and form in morphogenesis.
and differentiation. In Cold Spring Harbor Sympo- J. Math. Biol., 19: 265–279, 1984.
sium on Quant. Biol., volume 26, pages 389–401, [401] J. D. Murray and D. A. Smith.
rotational contribution to facilitated diffusion. J. [381] P. R. Montague and M. J. Friedlander. Morpho- theor. Biol., 118: 231–246, 1986.
genesis and territorial coverage by isolated mam- [402] J. D. Murray and J. Wyman. Facilitated diffusion: malian retinal ganglion cells.
J. Neurosci., 11: the case of carbon monoxide. J. Biol. Chem., 246: 1440–1457, 1991.
5903–5906, 1971.
[382] P. Morse and H. Feshbach. Methods of Theoretical [403] J. H. Myers and C. J. Krebs. Population cycles in Physics, volume 1. McGraw Hill, New York, 1953.
rodents. Sci. Amer., pages 38–46, June 1974.
[383] J. D. Murray. Singular perturbations of a class of [404] J. S. Nagumo, S. Arimoto, and S. Yoshizawa.
nonlinear hyperbolic and parabolic equations. J. An active pulse transmission line simulating nerve Maths. and Physics, 47: 111–133, 1968.
axon. Proc. IRE, 50: 2061–2071, 1962.
[384] J. D. Murray. Perturbation effects on the decay [405] V. Namias. Simple derivation of the roots of a cu- of discontinuous solutions of nonlinear first order bic equation. Am. J. Phys., 53: 775, 1985.
wave equations. SIAM J. Appl. Math., 19: 273– [406] E. G. Neal.
The Natural History of Badgers.
Croom Helm, Beckenham, UK, 1986.
[385] J. D. Murray. On the Gunn effect and other phys- [407] P. W. Nelson. Mathematical Models in Immunol- ical examples of perturbed conservation equations.
ogy and HIV Pathogenesis. PhD thesis, Depart- J. Fluid Mech., 44: 315–346, 1970b.
ment of Applied Mathematics, University of Wash- [386] J. D. Murray. On the molecular mechanism of facil- ington, Seattle, WA, 1998.
itated oxygen diffusion by haemoglobin and myo- [408] P. W. Nelson, A. S. Perelson, and J. D. Murray.
globin. Proc. R. Soc. Lond. B, 178: 95–110, 1971.
Delay model for the dynamics if HIV infection.
[387] J. D. Murray. On Burgers' model equations for Math. Biosci., 163: 201–215, 2000.
turbulence. J. Fluid Mech, 59: 263–279, 1973.
[409] J. C. Neu. Coupled chemical oscillators. SIAM J. [388] J. D. Murray. On a model for the temporal oscil- Appl. Math., 37: 307–315, 1979.
lations in the Belousov-Zhabotinskii reaction. J. [410] J. C. Neu. Large populations of coupled chemical Chem. Phys., 61: 3610–3613, 1974a.
SIAM J. Appl. Math., 38: 305–316, [389] J. D. Murray. On the role of myoglobin in muscle respiration. J. theor. Biol., 47: 115–126, 1974b.
[411] M. G. Neubert, M. Kot, and M. A. Lewis. Dis- [390] J. D. Murray. Non-existence of wave solutions for persal and pattern formation in a discrete-time a class of reaction diffusion equations given by the predatorprey model. Theor. Popul. Biol., 48: 7– volterra interacting-population equations with dif- fusion. J. theor. Biol., 52: 459–469, 1975.
[412] W. I. Newman. Some exact solutions to a nonlin- [391] J. D. Murray.
Nonlinear Differential Equation ear diffusion problem in population genetics and combustion. J. theor. Biol., 85: 325–334, 1980.
Comments Theor. Biol., 5: 175–282, [413] W. I. Newman. The long-time behaviour of solu- tions to a nonlinear diffusion problem in popula- [432] J. Panico and P. Sterling. Retinal neurons and ves- tion genetics and combustion. J. theor. Biol., 104: sels are not fractal but space-filling. J. Compar. 473–484, 1983.
Neurology, 361: 479–490, 1995.
[414] J. D. Nichols and R. H. Chabreck. On the variabil- [433] S. Parry, M. E. J. Barratt, S. Jones, S. McKee, ity of alligator sex ratios. American Nature, 116: and J. D. Murray. Modelling coccidial infection in 125–137, 1980.
chickens: emphasis on vaccination by in-feed deliv- [415] J. D. Nichols, L. Viehman, R. H. Chabreck, and ery of oocysts. J.theor. Biol., 157: 407–425, 1992.
B. Fenderson. Simulation of a commercially har- [434] D. Paumgartner, G. Losa, and E. R. Weibel. Reso- vested alligator population in Louisiana. La. Agr. lution effect on the stereological estimation of sur- Exp. Sta. Bull., 691: 1–59, 1976.
face and volume and its interpretation in terms [416] A. J. Nicholson.
An outline of the dynamics of of fractal dimension. J. Microscopy, 121: 51–63, animal population. Australian J. Zool., 2: 9–65, [435] R. Pearl. The Biology of Population Growth. Al- [417] A. J. Nicholson. The self adjustment of populations fred A. Knopf, New York, 1925.
to change. In Cold Spring Harbor Symposium on [436] H.-O. Peitgen, H. J¨ urgens, and D. Saupe. Chaos Quant. Biol., volume 22, pages 153–173, 1957.
and Fractals. Springer Verlag, New York, 1992.
[418] H. F. Nijhout. The Development and Evolution of [437] H.-O. Peitgen and P. H. Richter.
The Beauty Butterfly Wing Patterns. Smithsonian Institution of Fractals: Images of Complex Dynamical Sys- Press, Washington, D. C., 1991.
Springer Verlag, Berlin-Heidelberg-New [419] R. M. Nisbet and W. S. C. Gurney.
Fluctuating Populations. John Wiley, New York, [438] B. B. Peng, V. G´ ar, and K. Showalter. False bifurcations in chemical systems: canards. Phil. [420] M. A. Nowak, R. M. Anderson, M. R. Boerllist, Trans. R. Soc. Lond. A, 337: 275–289, 1991.
S. Bonhoeffer, R. M. May, and A. J. McMichael.
[439] A. S. Perelson, D. E. Kirschner, and R. De Boer.
HIV-1 evolution and disease progression. Science, Dynamics of HIV infection of CD4+ T cells. Math. 274: 1008–1010, 1996.
Biosci., 114: 81–125, 1993.
[421] G. Odell, G. F. Oster, B. Burnside, and P. Al- [440] A. S. Perelson and P. W. Nelson. Mathematical The mechanical basis for morphogenesis.
models of HIV-1 dynamics in vivo. SIAM Rev., Dev. Biol., 85: 446–462, 1981.
41: 3–44, 1999.
[422] G. M. Odell. Qualitative theory of systems of ordi- [441] A. S. Perelson, A. U. Neumann, M. Markowitz, J.
nary differential equations, including phase plane M. Leonard, and D. D. Ho. HIV-1 dynamics in analysis and the use of the Hopf bifurcation theo- vivo: Virion clearance rate, infected life-span, and rem. In L. A. Segel, editor, Mathematical Models viral generation time.
Science, 271: 1582–1586, in Molecular and Cellular Biology, pages 649–727.
Cambridge University Press, Cambridge, 1980.
[442] T. A. Peterman, D. P. Drotman, and J. W. Cur- [423] E. P. Odum. Fundamentals of Ecology. Saunders, Epidemiology of the acquired immunodefi- Philadelphia, 1953.
ciency syndrome (AIDS). Epidemiology Reviews, [424] A. Okubo.
Diffusion and Ecological Problems: 7: 7–21, 1985.
Mathematical Models. Springer-Verlag, Berlin-Hei- [443] F. Phelps. Optimal sex ratio as a function of egg delberg-New York, 1980.
incubation temperature in the crocodilians. Bull. [425] A. Okubo. Dynamical aspects of animal grouping: Math. Biol., 54: 123–148, 1992.
swarms, schools, flocks and herds. Adv. Biophys., [444] E. R. Pianka. Competition and niche theory. In 22: 1–94, 1986.
R. M. May, editor, Theoretical Ecology: Princi- [426] A. Okubo and H. C. Chiang. An analysis of the ples and Applications, pages 167–196. Blackwells kinematics of swarming of Anarete pritchardi Kim Scientific, Oxford, 1981.
(Diptera: Cecideomyiidae). Res. Popul. Ecol., 16: [445] H. M. Pinsker. Aplysia bursting neurons as en- 1–42, 1974.
dogenous oscillators. I. Phase response curves for [427] M. Oldstone. Viruses, Plagues, and History. Ox- pulsed inhibitory synaptic input. II. Synchroniza- ford University Press, New York, 1998.
tion and entrainment by pulsed inhibitory synaptic input. J. Neurophysiol., 40: 527–556, 1977.
[428] G. F. Oster.
Lectures in population dynamics.
[446] R. E. Plant. The effects of calcium++ on bursting In R. C. Di Prima, editor, Modern Modelling of neurons. Biophys. J., 21: 217–237, 1978.
Continuum Phenomena, volume 16 of Lectures in [447] R. E. Plant. Bifurcation and resonance in a model Appl. Math., pages 149–190. Amer. Math. Soc., for bursting nerve cells. J. Math. Biol., 11: 15–32, [429] H. Othmer. Interactions of reaction and diffusion [448] R. E. Plant and M. Mangel. Modelling and sim- in open systems. PhD thesis, Chem. Eng. Dept.
ulation in agricultural pest management. SIAM. and Univ. Minnesota, 1969.
Rev., 29: 235–361, 1987.
[430] H. G. Othmer, P. K. Maini, and J. D. Murray, ed- [449] J. C. F. Poole and A. J. Holladay.
itors. Mathematical Models for Biological Pattern and the Plague of Athens. Classical Quarterly, 29: Formation. Plenum Press, New York, 1993.
282–300, 1979.
[431] H. G. Othmer and P. Schaap. Oscillatory cAMP [450] A. C. Pooley. Nest opening response of the Nile signalling in the development of Dictyostelium dis- crocodile, Crocodylus niloticus.
J. Zool. Lond., 182: 17–26, 1977.
[451] A. C. Pooley and C. Gans. The Nile Crocodile.
ossler, O. E. Chemical turbulence: chaos in a Sci. Amer., 234: 114–124, 1976.
simple reaction-diffusion system.
Z. Naturfosch. [452] J. H. Powell. Bring Out Your Dead: The Great (A), 31: 1168–1172, 1976.
Plague of Yellow Fever in Philadelphia in 1793.
ossler, O. E. An equation for hyperchaos. Phys. University of Pennsylvania Press, Philadelphia, Lett. (A), 57: 155–157, 1979.
ossler, O. E. The chaotic hyerarchy. Z. Natur- [453] I. Prigogene and R. Lefever. Symmetry breaking fosch. (A), 38: 788–801, 1983.
instabilities in dissipative systems. II. J. Chem. [472] M. Rotenberg. Effect of certain stochastic param- Phys., 48: 1665–1700, 1968.
eters on extinction and harvested populations. J. [454] G. F. Raggett. Modelling the Eyam plague. Bull. theor. Biol., 124: 455–472, 1987.
Inst. Math. and its Applic., 18: 221–226, 1982.
[473] J. Roughgarden. Theory of Population Genetics [455] R. H. Rand, A. H. Cohen, and P. J. Holmes. Sys- and Evolutionary Ecology. Prentice-Hall, Engle- tems of coupled oscillators as models of CPG's. In wood Cliffs, NJ, 1996.
A. H. Cohen, S. Rossignol, and S. Grillner, editors, [474] R. Rubin, D. C. Leuker, J. O. Flom, and S. An- Neural Control of Rhythmic Movements in Ver- dersen. Immunity against Nematospiroides dubius tebrates, pages 333–368. John Wiley, New York, in CFW Swiss Webster mice protected by subcu- taneous larval vaccination. J. Parasitol., 57: 815– [456] R. H. Rand and P. J. Holmes. Bifurcation of pe- riodic motions in two weakly coupled van der Pol [475] S. I. Rubinow. Introduction to Mathematical Biol- oscillators. Int. J. Nonlinear Mech., 15: 387–399, ogy. John Wiley, New York, 1975.
[476] S. I. Rubinow and M. Dembo. The facilitated dif- [457] P. E. Rapp. Analysis of biochemical phase shift fusion of oxygen by haemoglobin and myoglobin.
oscillators by a harmonic balancing technique. J. Biophys. J., 18: 29–41, 1977.
Math. Biol., 3: 203–224, 1976.
[477] M. T. Sadler. The law of population a treatise, [458] E. Renshaw. Modelling Biological Populations in in six books: in disproof of the superfecundity of Space and Time.
Cambridge University Press, human beings, and developing the real principle of Cambridge, 1991.
their increase. J. Murray, London, 1830. In Cole.
[459] L. Rensing, U. an der Heiden, and M. C. Mackey, Q. Rev. Biol. 29: 103–137, 1954.
editors. Temporal Disorder in Human Oscillatory [478] A. N. Sarkovskii. Coexistence of cycles of a con- tinuous map of a line into itself (in Russian). Ukr. Mat. Z., 16: 61–71, 1964.
[460] T. Rhen and J. W. Lang. Phenotypic plasticity for [479] J. Satsuma. Explicit solutions of nonlinear equa- growth in the common snapping turtle: effects of tions with density dependent diffusion. J. Phys. incubation temperature, clutch and their interac- Soc. Japan, 56: 1947–1950, 1987.
tion. American Naturalist, 146: 727–747, 1995.
[480] W. M. Schaffer. Stretching and folding in lynx fur [461] W. E. Ricker. Stock and recruitment. J. Fisheries returns: evidence for a strange attractor in nature? Res. Board of Canada, 11: 559–623, 1954.
Amer. Nat., 24: 798–820, 1984.
[462] J. Rinzel. Models in neurobiology. In R. H. Enns, [481] W. M. Schaffer and M Kot. Chaos in ecological B. L. Jones, R. M. Miura, and S. S. Rangnekar, systems: the coals that Newcastle forgot. Trend editors, Nonlinear Phenomena in Physics and Bi- Ecol. Evol., 1: 58–63, 1986.
ology, pages 345–367. Plenum Press, New York, [482] A. Schierwagen. Scale-invariant diffusive growth: a dissipative principle relating neuronal form to [463] J. Rinzel. On different mechanisms for membrane In J. M. Smith and G. Vida, editors, potential bursting. In Proc. Sympos. on Nonlinear Organisational Constraints in the Dynamics of Oscillations in Biology and Chemistry, Salt Lake Evolution, pages 167–189. Manchester University City 1985, volume 66 of Lect. Notes in Biomathe- Press, Manchester, 1990.
matics, pages 19–33, Berlin-Heidelberg-New York, [483] J. Schnackenberg. Simple chemical reaction sys- tems with limit cycle behaviour. J. theor. Biol.81: [464] J. Rinzel and G. B. Ermentrout. Beyond a pace- 389–400, 1979.
maker's entrainment limit: phase walkthrough.
[484] M. C. Schuette and H. W. Hethcote. Modelling Am. J. Physiol., 246: R102–106, 1983.
the effects of varicella vaccination programs on the [465] G. B. Risse.
A long pull, a strong pull and all incidence of chickenpox and shingles. Bull. Math. together—San Francisco and bubonic plague 1907– Biol., 61: 1031–1064, 1999.
1908. Bull.Hist. Med., 66: 260–286, 1992.
[485] S. K. Scott. Chemical Chaos. Oxford University [466] D. V. Roberts. Enzyme Kinetics. Cambridge Uni- Press, Oxford, 1991.
versity Press, Cambridge, 1977.
[486] L. A. Segel.
Simplification and scaling.
[467] L. M. Rogers, R. Delahay, C. L. Cheeseman, S.
Rev., 14: 547–571, 1972.
Langton, G. C. Smith, and R. S. Clifton-Hadley.
[487] L. A. Segel, editor. Mathematical Models in Molec- Movement of badgers Meles meles in a high- ular and Cellular Biology. Cambridge University density population: individual, population and Press, Cambridge, 1980.
disease effects. Proc. R. Soc. Lond. B, 265: 1269– [488] L. A. Segel.
Modelling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge Uni- ossler, O. E. Chaotic behaviour in simple reac- versity Press, Cambridge, 1984.
tion systems.
Z. Naturfosch. (A), 31: 259–264, [489] L. A. Segel. On the validity of the steady state assumption of enzyme kinetics. Bull. Math. Biol., retical Ecology. Principles and Applications, pages 50: 579–593, 1988.
30–52. Blackwell Scientific, Oxford, second edition, [490] L. A. Segel and S. A. Levin. Application of non- linear stability theory to the study of the effects of [508] C. O. A. Sowunmi. Female dominant age-depen- diffusion on predator prey interactions. In R. A.
dent deterministic population dynamics. J. Math. Piccirelli, editor, Amer. Inst. Phys. Conf. Proc.: Biol., 3: 1–4, 1976.
Topics in Statistical Mechanics and Biophysics, [509] C. Sparrow. The Lorenz equations: Bifurcations, volume 27, pages 123–152, 1976.
chaos and strange attractors. In Appl. Math. Sci., [491] L. A. Segel and M. Slemrod. The quasi-steady state assumption: a case study in perturbation. SIAM. New York, 1982.
Rev., 31: 446–477, 1989.
[510] C. Sparrow.
The Lorenz equations. In A.V.
[492] N. Seiler, M. J. Jung, and J. K. Weser. Enzyme- Holden, editor, Chaos.
Manchester University activated Irreversible Inhibitors. Elsevier/North Press, Manchester, 1986.
Holland, Oxford, 1978.
[511] P. A. Spiro, J. S. Parkinson, and H. G. Othmer.
[493] F. R. Sharpe and A. J. Lotka. A problem in age A model of excitation and adaptation in bacterial distribution. Philos. Mag., 21: 435–438, 1911.
chemotaxis. Proc. Natl. Acad. Sci. USA, 94: 7263– [494] N. Shigesada. Spatial distribution of dispersing an- imals. J. Math. Biol., 9: 85–96, 1980.
[512] S. C. Stearns. Life history tactics: a review of the [495] N. Shigesada and K. Kawasaki. Biological Inva- ideas. Q. Rev. Biol., 51: 3–47, 1976.
sions: Theory and Practice.
Oxford University [513] P. Stefan. A theorem of Sarkovskii on the existence Press, Oxford, 1997.
of periodic orbits of continuous endomorphisms of [496] N. Shigesada, K. Kawasaki, and Y. Takeda. Mod- the real line. Comm. Math. Phys., 54: 237–248, eling stratified diffusion in biological invasions.
Amer. Naturalist, 146: 229–251, 1995.
[514] I. N. Steward and P. L. Peregoy. Catastrophe the- [497] N. Shigesada, K. Kawasaki, and E. Teramoto. Spa- ory modelling in perception. Psychological Bull., tial segregation of interacting species.
94: 336–362, 1988.
Biol., 79: 83–99, 1979.
[515] N. I. Stilianakis, C. A. B. Boucher, M. D. De- [498] N. Shigesada and J. Roughgarden.
Jong, R. VanLeeuwen, R. Schuurman, and R. J.
rapid dispersal in the population dynamics of com- DeBoer. Clinical data sets on human immunodefi- petition. Theor. Popul. Biol., 21: 353–372, 1982.
ciency virus type 1 reverse transcriptase resistant [499] K. Showalter and J. J. Tyson. Luther's 1906 dis- mutants explained by a mathematical model. J. covery and analysis of chemical waves. J. Chem. Virol., 71: 161–168, 1997.
Educ., 64: 742–744, 1987.
[516] N. I. Stilianakis, D. Schenzle, and K. Dietz. On [500] J. G. Skellam.
Random dispersal in theoretical the antigeneic diversity threshold model for AIDS.
populations. Biometrika, 38: 196–218, 1951.
Math. Biosci., 121: 235–247, 1994.
[501] J. G. Skellam. The formulation and interpretation [517] D. Stirzaker.
On a population model.
of mathematical models of diffusional processes in Biosc., 23: 329–336, 1975.
population biology. In M. S. Bartlett and R. W.
[518] S. H. Strogatz.
The mathematical structure of Hiorns, editors, The Mathematical Theory of the the human sleep-wake cycle.
In Lect. Notes Dynamics of Biological Populations, pages 63–85.
in Biomathematics, volume 69. Springer-Verlag, Academic Press, New York, 1973.
Berlin-Heidelberg-New York, 1986.
[502] A. F. G. Slater and A. E. Keymer.
[519] S. H. Strogatz. Nonlinear Dynamics and Chaos: mides polygyrus (Nematoda): the influence of di- with Applications in Physics, Biology, Chemistry, etary protein on the dynamics of repeated infec- tion. Proc. R. Soc. Lond. B, 229: 69–83, 1986.
Reading, MA, 1994.
[503] A. M. A. Smith and G. J. W. Webb. Crocodylus [520] S. H. Strogatz and I. Stewart. Coupled oscillators johnstoni in the McKinlay river area, N. T. VII.
and biological synchronization. Sci. Amer., 269: A population simulation model. Aust. Wild. Res., 102–109, 1993.
12: 541–554, 1985.
[521] F. A. Stuart, K. H. Mahmood, J. L. Stanford, and [504] G. D. Smith, L. J. Shaw, P. K. Maini, R. J. Ward, D. G. Pritchard. Development of diagnostic test P. J. Peters, and J. D. Murray. Mathemical mod- for, and vaccination against, tuberculosis in bad- elling of ethanol metabolism in normal subjects gers. Mammal Review, 18: 74–75, 1988.
and chronic alcohol misusers. Alcohol and Alco- [522] C. Taddei-Ferretti and L. Cordella. Modulation of holism, 28: 25–32, 1993.
Hydra attenuata rhythmic activity: phase response [505] H. L. Smith. Monotone Dynamical Systems; An curve. J. Exp. Biol., 65: 737–751, 1976.
Introduction to the Theory of Competitive and [523] S. Tatsunami, N. Yago, and M. Hosoe. Kinetics Cooperative Systems. Mathematical Surveys and of suicide substrates. Steady-state treatments and Monogrpahs 41. American Mathematical Society, computer-aided exact solutions. Biochim. Biophys. Providence, 1993.
Acta., 662: 226–235, 1981.
[506] W. R. Smith. Hypothalmic regulation of pituitary [524] M. Tauchi and R. H. Masland. The shape and ar- secretion of luteinizing hormone. II. Feedback con- rangement of the cholinergic neurons in the rabbit trol of gonadotropin secretion. Bull. Math. Biol., retina. Proc. R. Soc. Lond. B, 223: 101–119, 1984.
42: 57–78, 1980.
[525] M. Tauchi, K. Morigawa, and Y. Fukuda. Morpho- [507] T. R. E. Southwood. Bionomic strategies and pop- logical comparisons between outer and inner ram- ulation parameters. In R. M. May, editor, Theo- ifying aplha cells of the albino rat retina.
Brain Res., 88: 67–77, 1992.
mathematical and numerical investigation of a bi- [526] D. Thoenes. ‘Spatial oscillations' in the Zhabotin- ological phenomenon. PhD thesis, Department of skii reaction.
Nature (Phys. Sci.), 243: 18–20, Applied Mathematics, University of Washington, Seattle, WA, 1996.
[527] D. Thomas. Artificial enzyme membranes, trans- [544] R. C. Tyson, S. R. Lubkin, and J. D. Murray. A port, memory, and oscillatory phenomena. In D.
minimal mechanism for bacterial pattern forma- Thomas and J.-P. Kernevez, editors, Analysis and tion. Proc. R. Soc. Lond. B, 266: 299–304, 1998.
Control of Immobilized Enzyme Systems, pages [545] R. C. Tyson, S. R. Lubkin, and J. D. Murray.
115–150. Springer-Verlag, Berlin-Heidelberg-New Model and analysis of chemotactic bacterial pat- terns in liquid medium. J. Math. Biol., 38: 359– [528] J. H. M. Thornley. Mathematical Models in Plant Morphology. Academic Press, New York, 1976.
[546] A. Uppal, W. H. Ray, and A. B. Poore. The clas- [529] D. Tilman and P. Kareiva, editors. Spatial Ecol- sification of the dynamic behaviour of continuous ogy, The Role of Space in Population Dynamics stirred tank reactors-influence of reactor residence and Interspecific Interactions. Princeton Univer- time. Chem. Eng. Sci., 31: 205–214, 1976.
sity Press, NJ, Princeton, 1998.
[547] USDA. Bovine Tuberculosis: Still a Threat for US [530] E. Titchmarsh. Eigenfunctions Expansions Asso- Cattle Herds. Scientific report, US Dept. Agricul- ciated with Second-Order Differential Equations.
ture, Washington, 1982a.
Clarendon Press, Oxford, 1964.
[548] USDA. Bovine Tuberculosis Eradication: Uniform [531] R. T. Tranquillo and D. A. Lauffenburger. Conse- Methods and Rules. Scientific report, US Dept.
quences of chemosensory phenomena for leukocyte Agriculture, Washington, 1982b.
chemotactic orientation. Cell Biophys., 8: 1–46, [549] P. van den Driessche and X. Zou. Global attrac- tivity in delay Hopfield neural network models.
[532] R. T. Tranquillo and D. A. Lauffenburger. Anal- SIAMJ. Appl. Math., 58: 1878–1890, 1998.
ysis of leukocyte chemosensory movement.
[550] P.-F. Verhulst. Notice sur la loi que la population Biosci., 66: 29–38, 1988.
suit dans son accroissement. Corr. Math. et Phys., [533] A. M. Turing. The chemical basis of morphogen- 10: 113–121, 1838.
esis. Phil. Trans. R. Soc. Lond. B, 237: 37–72, [551] P.-F. Verhulst.
le loi d'accroissement de la population. Nouveau [534] J. J. Tyson.
The Belousov-Zhabotinskii Reac- emoires de l'Acad´ emie Royale des Sciences et tion, volume 10 of Lect. Notes in Biomathemat- Belles Lettres de Bruxelles, 18: 3–38, 1845.
ics. Springer-Verlag, Berlin-Heidelberg-New York, [552] J. L. Vincent and J. M. Skowronski, editors. Re- newable Resource Management, volume 40 of Lect. [535] J. J. Tyson. Analytical representation of oscilla- Notes in Biomathematics. Springer-Verlag, Berlin- tions, excitability and travelling waves in a realis- Heidelberg-New York, 1981.
tic model of the Belousov-Zhabotinskii reaction. J. [553] V. Volterra. Variazionie fluttuazioni del numero Chem. Phys., 66: 905–915, 1977.
d'individui in specie animali conviventi.
[536] J. J. Tyson. Periodic enzyme synthesis: reconsid- Acad. Lincei., 2: 31–113, 1926.
eration of the theory of oscillatory repression. J. fluctuations of a number of individuals in animal theor. Biol., 80: 27–38, 1979.
species living together. Translation by R. N. Chap- [537] J. J. Tyson. Scaling and reducing the Field-K¨ man. In: Animal Ecology. pp. 409–448. McGraw Noyes mechanism of the Belousov-Zhabotinskii re- Hill, New York, 1931.
action. J. Phys. Chem., 86: 3006–3012, 1982.
[554] H. von Foerster. Some remarks on changing pop- [538] J. J. Tyson. Periodic enzyme synthesis and oscil- ulations. In F. Stohlman, editor, The Kinetics of latory suppression: why is the period of oscillation Cellular Proliferation, pages 382–407. Grune and close to the cell cycle time? J. theor. Biol., 103: Stratton, New York, 1959.
313–328, 1983.
[555] H. T. Waaler and M. A. Piot. The use of an epi- [539] J. J. Tyson. A quantitative account of oscillations, demiological model for estimating the effectiveness bistability, and travelling waves in the Belousov- of tuberculosis control measures. Bull. WHO, 41: In R. J. Field and M.
75–93, 1969.
Burger, editors, Oscillations and Travelling Waves [556] S. Waley. Kinetics of suicide substrates. Biochem. in Chemical Systems, pages 92–144. John Wiley, J., 185: 771–773, 1980.
New York, 1985.
[557] S. Waley. Kinetics of suicide substrates. Practical [540] J. J. Tyson. Modeling the cell division cycle: cdc2 procedures for determining parameters. Biochem. and cyclin interactions.
Proc. Natl. Acad. Sci. J., 227: 843–849, 1985.
USA, 88: 7238–7232, 1991.
[558] C. T. Walsh. Suicide substrates, mechanism-based [541] J. J. Tyson. What everyone should know about enzyme inactivators: recent developments. Annu. the Belousov-Zhabotinsky reaction. In Frontiers in Rev. Biochem., 53: 493–535, 1984.
Mathematical Biology, volume 100 of Lect. Notes [559] C. T. Walsh, T. Cromartie, P. Marcotte, and R.
in Biomathematics, pages 569–587.
Suicide substrates for flavoprotein en- Verlag, Berlin-Heidelberg-New York, 1994.
zymes. Methods Enzymol., 53: 437–448, 1978.
[542] J. J. Tyson and H. G. Othmer. The dynamics of [560] J. A. Walsh and K. S. Warren.
feedback control circuits in biochemical pathways.
in developing countries. New Eng. J. Med., 301: Prog. Theor. Biol., 5: 1–62, 1978.
967–974, 1979.
[543] R. C. Tyson.
Pattern formation by E. coli- [561] P. Waltman. Competition models in population bi- ology. In CMBS Lectures, volume 45. SIAM Pub- [578] A. T. Winfree. The Geometry of Biological Time.
lications, Philadelphia, 1984.
Springer-Verlag, Berlin-Heidelberg-New York, 1st [562] S. Watts. Epidemics and History: Disease, Power, edition, 1980.
Yale University Press, New [579] A. T. Winfree. Human body clocks and the timing Haven, 1998.
of sleep. Nature, 297: 23–27, 1982.
[563] P. Watzlawick, J. H. Beavin, and D. D. Jackson.
[580] A. T. Winfree.
The rotor in reaction-diffusion Pragmatics of Human Communication.
problems and in sudden cardiac death. In M. Cos- New York, 1967.
nard and J. Demongeot, editors, Lect. Notes inBiomathematics (Luminy Symposium on Oscilla- tions, 1981), volume 49, pages 201–207, Berlin- [564] G. Webb, A. M. Beal, S. C. Manolis, and K. E.
Heidelberg-New York, 1983. Springer-Verlag.
Dempsy. The effects of incubation temperature on [581] A. T. Winfree. Sudden cardiac death: a problem sex determination and embryonic development rate in topology. Sci. Amer., 248(5): 144–161, 1983.
in Crocodylus johnstoni and C. porosus. In G. J.
[582] A. T. Winfree. The prehistory of the Belousov- W. Webb, S. C. Manolis, and P. J. Whitehead, Zhabotinskii oscillator. J. Chem. Educ., 61: 661– editors, Wildlife Management: Crocodiles and Al- ligators, pages 507–531.
Surrey Beatty, Sydney, [583] A. T. Winfree. The Timing of Biological Clocks.
Scientific American Books, Inc., New York, 1987.
[565] G. F. Webb. Theory of nonlinear age-dependent population dynamics. Marcel Dekker, New York, [584] A. T. Winfree. The Geometry of Biological Time.
[566] G. J. W. Webb and A. M. A. Smith. Sex ratio and Springer-Verlag, Berlin-Heidelberg-New York, 2nd survivorship in the Australian freshwater crocodile edition, 2000.
Crocodylus johnstoni. Symp. Zool. Soc. Lond., 52: [585] B. A. Wittenberg, J. B. Wittenberg, and P. R. B.
319–355, 1984.
Caldwell. Role of myoglobin in the oxygen sup- [567] G. J. W. Webb and A. M. A. Smith. Life history ply to red skeletal muscle. J. Biol. Chem., 250: parameters, population dynamics, and the man- 9038–9043, 1975.
agement of crocodilians.
In G. J. W. Webb, S.
[586] J. B. Wittenberg.
C. Manolis, and P. J. Whitehead, editors, Wildlife diffusion: role of myoglobin in oxygen entry into Crocodiles and Alligators, pages muscle. Physiol. Rev., 50: 559–636, 1970.
199–210. Surrey Beatty, Sydney, 1987.
[587] A. Woodward, T. Hines, C. Abercrombie, and C.
[568] L. M. Wein, R. M. D'Amato, and A. S. Perelson.
Hope. Spacing patterns in alligator nests. J. Her- Mathematical considerations of antiretroviral ther- petol., 18: 8–12, 1984.
apy aimed at HIV-1 eradication or maintenance of [588] D. E. Woodward and J. D. Murray. On the effect of low viral loads. J. theor. Biol., 192: 81–98, 1998.
temperature-dependent sex determination on sex- [569] R. Weiss. AIDS and the myths of denial. Science ratio and survivorship in crocodilians.
and Public Affairs (Royal Soc. (Lond.) and The Soc. Lond. B, 252: 149–155, 1993.
British Association), pages 40–44, 1996. October.
[589] D. E. Woodward, R. C. Tyson, J. D. Murray, E. O.
[570] R. H. Whittaker. Communities and Ecosystems.
Budrene, and H. Berg. Spatio-temporal patterns Macmillan, New York, second edition, 1975.
generated by Salmonella typhimurium. Biophysi- [571] M. D. Whorton, J. L. Haas, L. Trent, and O. Wong.
cal J., 68: 2181–2189, 1995.
Reproductive effects of sodium borates on male [590] J. Wyman. Facilitated diffusion and the possible employees: birth rate assessment. Occ. Environ. role of myoglobin as transport mechanism. J. Biol. Med., 51: 761–767, 1994.
Chem., 241: 115–121, 1966.
[572] T. Wibbels, J. J. Bull, and D. Crews. Chronology [591] G. Yagil and E. Yagil. On the relation between and morphology of temperature-dependent sex de- effector concentration and the rate of induced en- termination. J. Exp. Zool., 260: 371–381, 1991.
zyme synthesis. Biophys. J., 11: 11–27, 1971.
[573] T. Wibbels, J. J. Bull, and D. Crews. Tempera- [592] E. C. Zeeman. Catastrophe Theory. Selected Pa- ture-dependent sex determination: a mechanistic Addison-Wesley, Reading, MA, approach. J. Exp. Zool., 270: 71–78, 1994.
[574] J. L. Willems. Stability Theory of Dynamical Sys- [593] E. C. Zeeman. Sudden changes in perception. In tems. John Wiley and Sons, New York, 1970.
J. Petitot-Cocorda, editor, Logos et Th´ eories des [575] M. H. Williamson. Biological Invasions. Chapman Catastrophe, pages 298–309, Geneva, 1982. Patino.
and Hall, London, 1996.
Proc. Colloq., C´ erisy-la Salle.
[576] A. T. Winfree. An integrated view of the resetting [594] A. M. Zhabotinskii. Periodic processes of the ox- of a circadian clock. J. theor. Biol., 28: 327–374, idation of malonic acid in solution (Study of the kinetics of Belousov's reaction). Biofizika, 9: 306– [577] A. T. Winfree. Resetting biological clocks. Physics Today, 28: 34–39, 1975.



Tips and Tricks for the Care of NSG Mice Dominique Kagele, Ph.D. Technical Information Services The Jackson Laboratory's Mission Performing Research Investigating genetics and biology of human disease Providing Resources JAX® Mice Clinical & Research Services, bioinformatics data, technical publications and more…

January - February 2016 Information New $72m Outpatients facility for Christchurch Bariatric Management Innovation (BMI) initiative and news from around the nation Information for readers, subscribers and advertisersYou'll notice some changes to New Zealand Health & Hospital during 2016. These changes have been introduced to provide you with content that is more accessible and timely. Plus there is now no charge for you to download your copies of New Zealand Health and Hospital from