Asymptotic behavior of non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps

Volume 10, Issue 4, pp 2079--2093 http://dx.doi.org/10.22436/jnsa.010.04.62

Publication Date: April 20, 2017 Submission Date: October 11, 2016

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Authors

Yanhua Zhang - Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China. - University of Chinese Academy of Sciences, Beijing 100049, China. - College of Science, China University of Petroleum, Qingdao 266580, China.

Abstract

In this paper, a non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps is studied. Firstly, we show that this model has a unique global positive solution under certain conditions. Then, we discuss the sufficient conditions for stochastically ultimate boundedness and obtain the asymptotic behavior of the solution. Finally, sufficient criteria for extinction of all prey and predator species, stochastic weak persistence in the mean of prey species are established.

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Keywords

• Gilpin-Ayala predator-prey model
• jumps
• moment boundedness
• asymptotic behavior
• extinction.

MSC

•  60H10
•  92D25
•  34F05

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