Journal of Mathematical Biology

, Volume 3, Issue 1, pp 5–7 | Cite as

On the differential equations of species in competition

  • S. Smale


It is shown that the ordinary differential equation commonly used to describe competing species are compatible with any dynamical behavior provided the number of species in very large.


Differential Equation Stochastic Process Ordinary Differential Equation Dynamical Behavior Probability Theory 
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  1. [1]
    Hirsch, M., Smale, S.: Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic Press 1974.Google Scholar
  2. [2]
    Kolomogorov, A. N.: Sulla Teoria di Volterra della Lotta per l'Esistenza, Giorn. Istituto Ital. Attuari 7, 74–80 (1936).Google Scholar
  3. [3]
    May, R.: Stability and Complexity in Model Ecosystems. Princeton, N. J.: Princeton University Press 1973.Google Scholar
  4. [4]
    May, R., Leonard, W.: Nonlinear aspects of competition between three species. SIAM Jour. of Appl. Math. 29, 243–252 (1975).Google Scholar
  5. [5]
    Rescigno, A., Richardson, I.: The struggle for life: I, two species. Bull Math. Biophys. 29, 377–388 (1967).Google Scholar
  6. [6]
    Rescigno, A.: The struggle for life: II, three competitors. Bull. Math. Biophys. 30, 291–298 (1968).Google Scholar
  7. [7]
    Smale, S.: Differential Dynamical Systems, Bull. Amer. Math. Soc. 73, 747–817 (1967).Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • S. Smale
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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