Dynamics of stochastic hybrid Gilpin-Ayala system with impulsive perturbations

Abstract

This paper is mainly concerned with the dynamics of the stochastic Gilpin-Ayala model under regime switching with impulsive perturbations. The goal is to analyze the effects of Markov chain and impulse on the dynamics. Some asymptotic properties are considered and sufficient criteria for stochastic permanence, extinction, non-persistence in the mean and weak persistence are obtained. The critical value among the extinction, non-persistence in the mean and weak persistence is explored. Our results demonstrate that the dynamics of the model have close relations with the impulse and the stationary distribution of the Markov chain.

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

“…It is well known that Gilpin-Ayala competition model (GACM) has been hotly discussed (see in [1][2][3][4][5][6][7]) due to its importance in simulating two or more competing biological populations in nature. As diffusion is an essential characteristic of most biological populations, Ling Bai and Ke Wang began to investigate the global stability of reaction-diffusion Gilpin-Ayala ecosystem under Neumann zero boundary value in 2005 (see in [8]), and obtained good results.…”

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

“…It is well known that Gilpin-Ayala competition model (GACM) has been hotly discussed (see [1][2][3][4][5][6][7]) due to its importance in simulating two or more competing biological populations in nature. Since diffusion is an essential characteristic of most biological populations, Ling Bai and Ke Wang began to investigate the global stability of reaction-diffusion Gilpin-Ayala ecosystem under Neumann zero boundary value in 2005 (see [8]), and obtained good results.…”

Dynamics of a stochastic Gilpin–Ayala population model with Markovian switching and impulsive perturbations

“…In recent years, the stability of impulsive differential equations and the existence and stability of periodic solutions of periodic systems have been studied systematically. Wu [28] considered the Gilpin-Ayala model under regime switching with impulsive effects:…”