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Stationary distribution of a stochastic predator–prey system with stage structure for prey

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  • Zhao, Xin
  • Zeng, Zhijun

Abstract

In this paper, a predator–prey model with stage structure is proposed and analyzed in which preys are divided into juvenile and mature preys from a deterministic framework to a stochastic one. We first prove that the system which we investigate has a unique global positive solution. Furthermore, we obtain the sufficient criteria for the existence of stationary distribution and ergodicity by constructing an appropriate Lyapunov function, which means the species are permanent. Finally, we give the sufficient conditions for extinction of preys.

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  • Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution of a stochastic predator–prey system with stage structure for prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119318588
    DOI: 10.1016/j.physa.2019.123318
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    References listed on IDEAS

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    1. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and higher order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 467-475.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    3. Lu, Yang & Pawelek, Kasia A. & Liu, Shengqiang, 2017. "A stage-structured predator-prey model with predation over juvenile prey," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 115-130.
    4. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    5. 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.
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    7. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    8. Li, Haihong & Cong, Fuzhong, 2019. "Dynamics of a stochastic Holling–Tanner predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
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    Cited by:

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    2. Cao, Nan & Fu, Xianlong, 2023. "Stationary distribution and extinction of a Lotka–Volterra model with distribute delay and nonlinear stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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