Simple mathematical models with very complicated dynamics

Nature - Tập 261 Số 5560 - Trang 459-467 - 1976
Robert M. May1,2
1King’s College Research Centre
2Princeton University

Tóm tắt

Từ khóa


Tài liệu tham khảo

May, R. M., and Oster, G. F., Am. Nat., 110 (in the press).

Varley, G. C., Gradwell, G. R., and Hassell, M. P., Insect Population Ecology (Blackwell, Oxford, 1973).

May, R. M., (ed.), Theoretical Ecology: Principles and Applications (Blackwell, Oxford, 1976).

Guckenheimer, J., Oster, G. F., and Ipaktchi, A., Theor. Pop. Biol. (in the press).

Oster, G. F., Ipaktchi, A., and Rocklin, I., Theor. Pop. Biol. (in the press).

Asmussen, M. A., and Feldman, M. W., J. theor. Biol. (in the press).

Hoppensteadt, F. C., Mathematical Theories of Populations: Demographics, Genetics and Epidemics (SIAM, Philadelphia, 1975).

Samuelson, P. A., Foundations of Economic Analysis (Harvard University Press, Cambridge, Massachusetts, 1947).

Goodwin, R. E., Econometrica, 19, 1–17 (1951).

Baumol, W. J., Economic Dynamics, 3rd ed. (Macmillan, New York, 1970).

See, for example, Kemeny, J., and Snell, J. L., Mathematical Models in the Social Sciences (MIT Press, Cambridge, Massachusetts, 1972).

Chaundy, T. W., and Phillips, E., Q. Jl Math. Oxford, 7, 74–80 (1936).

Myrberg, P. J., Ann. Akad. Sc. Fennicae, A, I, No. 336/3 (1963).

Myrberg, P. J., Ann. Akad. Sc. Fennicae, A, I, No. 259 (1958).

Lorenz, E. N., J. Atmos. Sci., 20, 130–141 (1963); Tellus, 16, 1–11 (1964).

Metropolis, N., Stein, M. L., and Stein, P. R., J. Combinatorial Theory, 15(A), 25–44 (1973).

Maynard Smith, J., Mathematical Ideas in Biology (Cambridge University Press, Cambridge, 1968).

Krebs, C. J., Ecology (Harper and Row, New York, 1972).

May, R. M., Am. Nat., 107, 46–57 (1972).

Li, T.-Y., and Yorke, J. A., Am. Math. Monthly, 82, 985–992 (1975).

Hoppensteadt, F. C., and Hyman, J. M., (Courant Institute, New York University: preprint, 1975).

Smale, S., and Williams, R.,(Department of Mathematics, Berkeley: preprint, 1976).

May, R. M., Science, 186, 645–647 (1974).

Moran, P. A. P., Biometrics, 6, 250–258 (1950).

Ricker, W. E., J. Fish. Res. Bd. Can., 11, 559–623 (1954).

Cook, L. M., Nature, 207, 316 (1965).

Macfadyen, A., Animal Ecology: Aims and Methods (Pitman, London, 1963).

May, R. M., J. theor. Biol., 51, 511–524 (1975).

Guckenheimer, J., Proc. AMS Symposia in Pure Math., XIV, 95–124 (1970).

Gilbert, E. N., and Riordan, J., Illinois J. Math., 5, 657–667 (1961).

Preston, C. J., (King's College, Cambridge: preprint, 1976).

Gumowski, I., and Mira, C., C. r. hebd. Séanc. Acad. Sci., Paris, 281a, 45–48 (1975); 282a, 219–222 (1976).

Layzer, D., Sci. Am., 233(6), 56–69 (1975).

Ulam, S. M., Proc. Int. Congr. Math. 1950, Cambridge, Mass.

Vol. II, pp. 264-273 (AMS, Providence R. I., 1950).

Ulam, S. M., and von Neumann, J., Bull. Am. math. Soc. (abstr.), 53, 1120 (1947).

Kac, M., Ann. Math., 47, 33–49 (1946).

May, R. M., Science, 181, 1074 (1973).

Hassell, M. P., J. Anim. Ecol., 44, 283–296 (1974).

Hassell, M. P., Lawton, J. H., and May, R. M., J. Anim. Ecol. (in the press).

Ruelle, D., and Takens, F., Comm. math. Phys., 20, 167–192 (1971).

Landau, L. D., and Lifshitz, E. M., Fluid Mechanics (Pergamon, London, 1959).

Martin, P. C., Proc. Int. Conf. on Statistical Physics, 1975, Budapest (Hungarian Acad. Sci., Budapest, in the press).

Southwood, T. R. E., in Insects, Science and Society (edit. by Pimentel, D.), 151–199 (Academic, New York, 1975).

Metropolis, N., Stein, M. L., and Stein, P. R., Numer. Math., 10, 1–19 (1967).

Gumowski, I., and Mira, C., Automatica, 5, 303–317 (1969).

Stein, P. R., and Ulam, S. M., Rosprawy Mat., 39, 1–66 (1964).

Beddington, J. R., Free, C. A., and Lawton, J. H., Nature, 255, 58–60 (1975).

Hirsch, M. W., and Smale, S., Differential Equations, Dynamical Systems and Linear Algebra (Academic, New York, 1974).

Kolata, G. B., Science, 189, 984–985 (1975).

Smale, S., (Department of Mathematics, Berkeley: preprint, 1976).

May, R. M., and Leonard, W. J., SIAM J. Appl. Math., 29, 243–253 (1975).