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The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching

Author

Listed:
  • Chen, Zhewen
  • Tian, Zhuyan
  • Zhang, Shuwen
  • Wei, Chunjin

Abstract

This paper addresses a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching. The stochastic model in this paper includes white and colored noises. For the model, we first prove the existence of the global positive solution of the model. And then by using Khasminskii’s method and Lyapunov function, we derive sufficient conditions for the existence of a unique ergodic stationary distribution. Finally, numerical simulations are carried out to support our results.

Suggested Citation

  • Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315523
    DOI: 10.1016/j.physa.2019.122728
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    References listed on IDEAS

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    1. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
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    3. Zhang, Jia-Fang & Wang, Shaoli & Kong, Xiangjun, 2018. "Effects of toxin delay on the dynamics of a phytoplankton–zooplankton model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1150-1162.
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    7. Huo, Hai-Feng & Yang, Peng & Xiang, Hong, 2018. "Stability and bifurcation for an SEIS epidemic model with the impact of media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 702-720.
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    10. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
    11. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
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    Cited by:

    1. 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.
    2. Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Chen, Zhewen & Zhang, Ruimin & Li, Jiang & Zhang, Shuwen & Wei, Chunjin, 2020. "A stochastic nutrient-phytoplankton model with viral infection and Markov switching," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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