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Periodic measure of a stochastic non-autonomous predator–prey system with impulsive effects

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  • Yang, Jiangtao

Abstract

In this paper, we study a stochastic predator–prey system with impulsive effects and time periodic coefficients. By the properties of periodic Markov processes, Krylov–Bogolyubov’s method and Doob’s Theorem, the existence and uniqueness of periodic measure of the system is presented under the condition of the stochastic persistence of the system. Numerical simulations are given to verify the effectiveness of the theoretical results and to show the effects of the stochastic perturbation and impulsive perturbation on the persistence and periodic measure of the system.

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  • Yang, Jiangtao, 2022. "Periodic measure of a stochastic non-autonomous predator–prey system with impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 464-479.
    • Handle: RePEc:eee:matcom:v:202:y:2022:i:c:p:464-479
    DOI: 10.1016/j.matcom.2022.06.011
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    References listed on IDEAS

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    1. Jiang, Daqing & Zuo, Wenjie & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Stationary distribution and periodic solutions for stochastic Holling–Leslie predator–prey systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 16-28.
    2. Yang, Jiangtao, 2020. "Threshold behavior in a stochastic predator–prey model with general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Miao Zhang & Gaofeng Zong, 2015. "Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2371-2384, June.
    4. Lu, Chun & Ding, Xiaohua, 2019. "Periodic solutions and stationary distribution for a stochastic predator-prey system with impulsive perturbations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 313-322.
    5. Wang, Feng-Yu & Yuan, Chenggui, 2011. "Harnack inequalities for functional SDEs with multiplicative noise and applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2692-2710, November.
    6. Li, Dingshi & Lin, Yusen, 2021. "Periodic measures of impulsive stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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    Cited by:

    1. Wang, Zhaojuan & Liu, Meng, 2023. "Periodic measure of a stochastic single-species model in periodic environments," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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