Stochastic permanence and extinction for one-dimensional stochastic Gilpin-Ayala systems with Markovian switching

Abstract

In this paper, we consider the permanence, extinction for one-dimensional stochastic Gilpin-Ayala system with Markovian switching. By using Lyapunov method and some novel techniques, some sufficient conditions are obtained which ensure the permanence, extinction for the system. In the case of η = 1, sufficient and necessary conditions for permanence and extinction are obtained. Two numerical examples are provided to illustrate the effectiveness and the benefits of the proposed result.