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.
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