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