On stochastic Gilpin–Ayala population model with Markovian switching

In this paper, we analyze a stochastic Gilpin–Ayala population model with Markovian switching and white noise. The Gilpin–Ayala parameter is also allowed to switch. We establish the global stability of the trivial equilibrium state of the model. Verifiable sufficient conditions which guarantee the extinction and persistence are provided. Furthermore, we show the existence of a stationary distribution. The analytical results are illustrated by computer simulations.