Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise

Wang, Sheng; Wang, Linshan; Wei, Tengda

Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise

Sheng Wang, Linshan Wang and Tengda Wei

Physica A: Statistical Mechanics and its Applications, 2018, vol. 495, issue C, 294-311

Abstract: This paper concerns the dynamics of a stochastic predator–prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global positive solution to the system is proved. Then, by combining stochastic analytical techniques with M-matrix analysis, sufficient conditions of stochastic permanence and extinction are obtained. Furthermore, for the stochastic permanence case, by means of four constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated. Finally, our conclusions are illustrated through an example.

Keywords: Stochastic permanence; Markov chain; Lévy noise; Predator–prey; Beddington–DeAngelis (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:495:y:2018:i:c:p:294-311

DOI: 10.1016/j.physa.2017.12.088

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