Stability and dynamical bifurcation of a stochastic regime-switching predator–prey model

Abstract

This paper considers a stochastic regime-switching predator–prey system with general functional response. We show that the system exactly possesses two dynamical bifurcation points (DBPs), and the expressions of these DBPs are given explicitly. In addition, we provide the sharp sufficient criteria under which the system admits a unique ergodic invariant measure (UEIM), and show that the transition function of the solution of the system exponentially converges to the UEIM under the total variation norm. The findings show that the stability and dynamical bifurcation of the system have close relationships with the random perturbations. Additionally, the main findings are applied to several special cases, and a number of recent reports are improved.