Stability and ergodicity of a stochastic Gilpin–Ayala model under regime switching on patches

The purpose of this work is to investigate the asymptotic properties of a stochastic Gilpin–Ayala population system under regime switching on patches. We establish the global stability and the extinction of the trivial equilibrium state of the model. Furthermore, we show the existence of the stationary distribution for our system model. The analytical results are illustrated by computer simulations.