Permanence and extinction of regime-switching predator-prey models

TL;DR

This paper investigates the conditions under which predator and prey populations persist or go extinct in a model that accounts for random environmental changes using regime-switching dynamics.

Contribution

It introduces sharp criteria for permanence and extinction in regime-switching predator-prey models with Beddington-DeAngelis response, extending known results to stochastic environments.

Findings

Criteria for prey extinction in certain environments

Conditions for prey persistence despite environmental variability

Extension of on-off permanence results to stochastic switching models

Abstract

In this work we study the permanence and extinction of a regime-switching predator-prey model with Beddington-DeAngelis functional response. The switching process is used to describe the random changing of corresponding parameters such as birth and death rates of a species in different environments. Our criteria can justify whether a prey die out or not when it will die out in some environments and will not in others. Our criteria are rather sharp, and they cover the known on-off type results on permanence of predator-prey models without switching. Our method relies on the recent study of ergodicity of regime-switching diffusion processes.