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

TL;DR

This paper investigates the long-term behavior of a stochastic Gilpin-Ayala population model with regime switching and noise, establishing conditions for stability, persistence, extinction, and stationary distribution, thus extending existing theoretical results.

Contribution

It provides new conditions for stochastic permanence and stationary distribution, generalizing previous findings in the literature.

Findings

Proved existence of global positive solutions.

Established asymptotic stability in probability.

Derived conditions for stochastic permanence and stationary distribution.

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, $p$th 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.