Analysis of a nonautonomous stochastic predator-prey model with Crowley-Martin functional response

Yan Zhang,Shihua Chen,Shujing Gao

doi:10.1186/s13662-016-0993-1

Yan Zhang, Shihua Chen + Show 1 more

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https://doi.org/10.1186/s13662-016-0993-1

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Abstract

The objective of this paper is to study some qualitative dynamic properties of a nonautonomous predator-prey model with stochastic perturbation and Crowley-Martin functional response. The existence of a global positive solution and stochastically ultimate boundedness are obtained. Sufficient conditions for extinction, persistence in the mean, and stochastic permanence of the system are established. We also derive conditions to guarantee the global attractiveness and stochastic persistence in probability of the model. Our theoretical results are confirmed by numerical simulations.

Highlights

1 Introduction Predator-prey systems play an important role in studying the dynamics of interacting species
Many researchers have paid their attention to predatorprey systems with prey-dependent functional response
3 Persistence and extinction In this part, we show the long-time dynamical properties of system ( ), including extinction, persistence in the mean, and stochastic permanence in Theorems

Summary

Introduction

Predator-prey systems play an important role in studying the dynamics of interacting species. In accordance with system ( ), we propose the following stochastic predator-prey model: ω(t)y dx = x r(t) – k(t)x – In Section , we obtain sufficient conditions for extinction, persistence in the mean, and stochastic permanence.

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