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

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  • Wang, Sheng
  • Wang, Linshan
  • Wei, Tengda

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.

Suggested Citation

  • Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    • Handle: RePEc:eee:phsmap:v:495:y:2018:i:c:p:294-311
    DOI: 10.1016/j.physa.2017.12.088
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    References listed on IDEAS

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    1. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    2. Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, March.
    3. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
    4. Ouyang, Mengqian & Li, Xiaoyue, 2015. "Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 539-559.
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