Dynamic behavior of stochastic predator-prey system

Abstract

In this paper, a stochastic predator-prey system with mutual interference is studied, which provides guidance on creating appropriate biodegradable environments. By utilizing Mawhin's coincidence degree theorem and constructing a suitable Lyapunov function, a Volterra model with mutual interference is studied. A few sufficient conditions are obtained for existence, extinction and global asymptomatic stability of the positive solution of the model. Then we perform various numerical simulations to verify the stochastic and deterministic systems are global asymptotically stable. It is significant that such a model is firstly proposed with stochastic mutual interference.