Stationary distribution of a stage-structure predator–prey model with prey’s counter-attack and higher-order perturbations

Abstract

In this paper, we investigate a stochastic predator–prey model with counter-attacking behavior which means the prey can attack juvenile predator. We establish the sufficient conditions for the existence of a unique ergodic stationary distribution by constructing a series of Lyapunov functions. From the biological point of view, the ergodic results enable us to predict whether the system is generally stable in the long term.