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Multiple stable equilibria in a predator-prey system. (English) Zbl 0585.92023

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.

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:
92D40Ecology
92D25Population dynamics (general)
34C99Qualitative theory of solutions of ODE