Stochastic Periodic Solution and Permanence of a Holling–Leslie Predator-Prey System with Impulsive Effects

Considering the environmental effects, a Holling–Leslie predator-prey system with impulsive and stochastic disturbance is proposed in this paper. Firstly, we prove that existence of periodic solution, the mean time boundness of variables is found by integral inequality, and we establish some suffici...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2021; pp. 1 - 19
Main Authors Zhao, Jinxing, Shao, Yuanfu
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2021
John Wiley & Sons, Inc
Wiley
Subjects
Differential equations
Endangered & extinct species
Environmental effects
Integral equations
Mathematics
Noise
Predator-prey simulation
Random variables
Stochastic models
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Summary:Considering the environmental effects, a Holling–Leslie predator-prey system with impulsive and stochastic disturbance is proposed in this paper. Firstly, we prove that existence of periodic solution, the mean time boundness of variables is found by integral inequality, and we establish some sufficient conditions assuring the existencle of periodic Markovian process. Secondly, for periodic impulsive differential equation and system, it is different from previous research methods, by defining three restrictive conditions, we study the extinction and permanence in the mean of all species. Thirdly, by stochastic analysis method, we investigate the stochastic permanence of the system. Finally, some numerical simulations are given to illustrate the main results.
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ISSN:2314-4629
2314-4785
DOI:10.1155/2021/6694479