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Dynamics of a two-predator one-prey stochastic delay model with Lévy noise

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  • Wu, Jian

Abstract

In this paper, the stability in distribution of the solutions (SDS) of a two-predator one-prey stochastic delay model with Lévy noise is considered. We show that under some simple conditions, the complete dynamic scenarios of SDS are characterized by three parameters η1>η2>η3, which depend on the interaction and Lévy noise. We prove that if η1<1, then limt→+∞yi(t)=0 almost surely, i=1,2,3; if ηi>1>ηi+1, then limt→+∞yj(t)=0 almost surely, j=i+1,…,3, and the distributions of (y1(t),⋯,yi(t))T converge weakly to a unique ergodic invariant distribution (UEID); if η3>1, then the distributions of (y1(t),y2(t),y3(t))T converge weakly to a unique ergodic invariant distribution (UEID).

Suggested Citation

  • Wu, Jian, 2020. "Dynamics of a two-predator one-prey stochastic delay model with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    • Handle: RePEc:eee:phsmap:v:539:y:2020:i:c:s0378437119316516
    DOI: 10.1016/j.physa.2019.122910
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    References listed on IDEAS

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    1. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.
    2. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    3. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    4. 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.
    5. Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
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