Long-Time Behaviours of a Stochastic Predator-Prey System with Holling-Type II Functional Response and Regime Switching

Weili Kong,Yuanfu Shao,Stanislaw Migorski

doi:10.1155/2021/6672030

Weili Kong, Yuanfu Shao + Show 1 more

Open Access

https://doi.org/10.1155/2021/6672030

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Abstract

Considering the impacts of white noise, Holling-type II functional response, and regime switching, we formulate a stochastic predator-prey model in this paper. By constructing some suitable functionals, we establish the sufficient criteria of the stationary distribution and stochastic permanence. By numerical simulations, we illustrate the results and analyze the influence of regime switching on the dynamics.

Highlights

Functional responses are very important in the predatorprey system, which is the amount of prey catch per predator per unit of time and has significant effect on the dynamical properties
May reveals that due to stochastic fluctuations in environmental conditions, all the natural parameters exhibit a certain amount of random perturbations, and random disturbance is introduced in many mathematical models to reveal the effect of white noise [10,11,12,13,14,15]
We study a stochastic predator-prey system with regime switching and Holling-type II functional responses. eorems 1 and 2 give the sufficient conditions of stationary distribution and the stochastic permanence of (2)

Summary

Introduction

Functional responses are very important in the predatorprey system, which is the amount of prey catch per predator per unit of time and has significant effect on the dynamical properties. May reveals that due to stochastic fluctuations in environmental conditions, all the natural parameters exhibit a certain amount of random perturbations, and random disturbance is introduced in many mathematical models to reveal the effect of white noise [10,11,12,13,14,15]. The growth of species suffers from fluctuating environments such as hurricanes and earthquakes, which is described by colorful noise in mathematical modelling [16,17,18]. In this article, we formulate a stochastic model with Holling-type II functional response and colorful noise.

The Model and Notations

Stationary Distribution

Stochastic Permanence

Examples and Simulations

Conclusions and Discussion