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Dynamical behavior of a one predator and two independent preys system with stochastic perturbations

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  • Ji, Chunyan
  • Jiang, Daqing
  • Lei, Dongxia

Abstract

A one predator and two independent preys system with stochastic perturbations is considered. First, we show that there is a positive solution of this system. Then, we investigate the long time behavior of this system. Sufficient criteria for extinction and persistence in time average are established. Moreover, it is also shown that this system has a stationary distribution and it is ergodicity. Finally, examples and simulations are carried on to verify these results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:649-664
    DOI: 10.1016/j.physa.2018.10.006
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    References listed on IDEAS

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    1. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    2. Zhang, Qiumei & Jiang, Daqing, 2015. "The coexistence of a stochastic Lotka–Volterra model with two predators competing for one prey," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 288-300.
    3. Haihong Li & Daqing Jiang & Fuzhong Cong & Haixia Li, 2014. "Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    4. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

    1. 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).
    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).
    3. Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.

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