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Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment

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  • Yu, Xingwang
  • Yuan, Sanling
  • Zhang, Tonghua

Abstract

To theoretically address the effects of random environmental change on the growth of plankton, we propose a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton and Markov switching in an impulsive polluted environment. We then analyse the extinction and persistence in mean, including weak persistence and non-persistence. By constructing Lyapunov function, we can show the model can be positive recurrent or ergodic. To conclude our study, we carry out some simulations, indicating that environmental fluctuations and exogenous toxicant input have a great influence on the survival fate of plankton.

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  • Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:249-264
    DOI: 10.1016/j.amc.2018.11.005
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    References listed on IDEAS

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    7. 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.
    8. Zhao, Shengnan & Yuan, Sanling & Zhang, Tonghua, 2022. "The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
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    10. Kirkow, Velizar & Wang, Hao & Garcia, Pablo Venegas & Ahmed, Shohel & Heggerud, Christopher M., 2022. "Impacts of a changing environment on a stoichiometric producer-grazer system: a stochastic modelling approach," Ecological Modelling, Elsevier, vol. 469(C).
    11. Lifan Chen & Xingwang Yu & Sanling Yuan, 2022. "Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
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    13. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    14. 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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