Yihan Zhao, Yuanpei Xia, Zhichun Yang
Abstract:
In this article, we propose a three-species prey-predator system with Holling II
functional response and stochastic perturbations involving white noise and
Levy noise. Firstly, we study the existence and uniqueness of a global positive
solution and stochastic ultimate boundedness. Then, we obtain sufficient conditions
for stability, extinction, strongly persistence in the mean and stochastic permanence
in the sense of probability for the stochastic system.
The results show that both white noise and Levy noise may change the asymptotic
properties of the population system. Finally, some examples that chaotic dynamics
can be influenced by stochastic noises.
Submitted February 6, 2020. Published July 6, 2020.
Math Subject Classifications: 34D20, 92D25, 60H10.
Key Words: Predator-prey system; Levy noise; white noise; extinction;
stochastic permanence.
DOI: 10.58997/ejde.2020.71
Show me the PDF file (328 KB), TEX file for this article.
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Yihan Zhao School of Mathematics Chongqing Normal University Chongqing 401331, China email: zhaoyihan13@126.com |
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Yuanpei Xia School of Mathematics Chongqing Normal University Chongqing 401331, China email: xiayuanppei@163.com |
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Zhichun Yang School of Mathematics Chongqing Normal University Chongqing 401331, China email: yangzhch@126.com |
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