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Zbl 0585.92023
Harrison, Gary W.
Multiple stable equilibria in a predator-prey system. (English)
[J] Bull. Math. Biol. 48, 137-148 (1986). ISSN 0092-8240; ISSN 1522-9602/e

Summary: Necessary and sufficient conditions are given for three equilibria to occur in a predator-prey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. \par A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.

MSC 2000:: *92D40 Ecology
92D25 Population dynamics
34C99 Qualitative theory of solutions of ODE

Keywords: multiple stable equilibria; predator-prey model; predator intraspecific competition

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Zentralblatt MATH Berlin [Germany]