Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator

Abstract

In this paper, we deal with a stochastic predator–prey model with stage structure for predator population and ratio-dependent functional response. The proposed mathematical model consists of a system of three stochastic differential equations to stimulate the interactions between prey population, immature predator and mature predator population. We first establish sufficient conditions for the existence and uniqueness of the positive solutions by constructing an appropriate Lyapunov function. Then we extend the existence of stationary distribution under certain parametric restrictions. We also obtain the sufficient conditions for extinction of the predator populations. Finally, numerical simulations have been carried out to validate our analytical findings.