Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

Abstract

In this paper, a stochastic Gilpin–Ayala population model with regime switching and white noise is considered. All parameters are influenced by stochastic perturbations. The existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model are investigated, which generalize some results in the literatures. Moreover, the conditions presented for the stochastic permanence and the existence of stationary distribution improve the previous results.