Only mimic-species can survive when external noises are added in a ratio-dependent community dynamics model

Abstract

In this paper, we present a ratio-dependent community dynamics model on Batesian mimicry. In ecology, Batesian mimicry is very important which focus mainly on the patterns in model-species and the mimic-species. Here, we study a stochastically forced basic model-mimic community dynamics model. Without any environmental noise, both model-species and mimic-species can survive. However, external noises push the model-species to extinct and only mimic-species can stable. We discuss a mechanism of the noise-induced transition in the basin of attraction of a stable interior equilibrium point. We apply the stochastic sensitivity function technique to construct a confidence domain near a stable interior equilibrium point and study different noise intensity for the transition.