Electron. J. Differential Equations, Vol. 2020 (2020), No. 71, pp. 1-17
Asymptotic behavior of stochastic three-species predator-prey systems
with white and Levy noise
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
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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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