Dynamic equilibrium under periodic perturbations in simple ecosystem models

Abstract

Simple models of two-species ecosystems are usually analyzed in terms of the existence and stability of a static equilibrium state. We examine the way in which perturbations, in the form of periodic reductions in both species, lead to stable coexistence in a state of dynamic equilibrium. We establish general criteria for the occurrence of such dynamic equilibrium states. We show that coexistence in a dynamic equilibrium occurs for a fairly wide range of model parameters, and that dynamic equilibrium states are a rather robust feature of simple models.