Stationary distribution and ergodicity of a stochastic multi-species model with Holling type II response function

Abstract

In this paper, we consider a stochastic multi-species model with the Holling type II functional response, which includes the stochastic competition model, the stochastic mutualism model, and the stochastic hybrid model of competition and mutualism. Sufficient conditions for the stationary distribution and ergodicity of the model are established. We support our analytical findings through extensive simulation studies. We show that under relatively small noise, the model has a stationary distribution and ergodicity, while the relatively large noise leads to the non-persistent and non-stationary distribution of the model through the numerical simulation studies of three species.