Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations.

Abstract In this paper, we study a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations. We obtain the ergodic property by constructing a suitable stochastic Lyapunov function with regime-switching, which provides us a biological perspective of cycling phenomena of a population system, and can better describe the stochastic persistence of a population system in practice. We find that these restrictive assumptions on the functional response are relative weak and valid for many types of response functions. Highlights • A regime-switching predator–prey model with anti-predator behaviour is studied. • We obtain the ergodic property by constructing a suitable stochastic Lyapunov function. • The existence of a stationary distribution implies stochastic weak stability. [ABSTRACT FROM AUTHOR]