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A stochastic nutrient-phytoplankton model with viral infection and Markov switching

Author

Listed:
  • Chen, Zhewen
  • Zhang, Ruimin
  • Li, Jiang
  • Zhang, Shuwen
  • Wei, Chunjin

Abstract

In this paper, we extend a nutrient-phytoplankton model with viral infection from a deterministic model to a stochastic model by introducing white noise and color noise. We analyze this model mainly from the perspectives of mathematics and biology. Mathematically, we get a critical value. In the case of low white noise intensity, if this critical value is less than one, the infected phytoplankton tend to die out exponentially. If this critical value is greater than one, the infected phytoplankton is persistent in mean and the solution of system is positive recurrent. From a biological standpoint, we show that white noise may have negative effect on population survival, while Markov chain can balance the different survival states of the population and increase its survival probability, which can provide effective measures to control the infected phytoplankton and ensure the stationary distribution of the population in reality.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305063
    DOI: 10.1016/j.chaos.2020.110109
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    References listed on IDEAS

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    1. 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).
    2. Chunjin Wei & Yingjie Fu, 2020. "Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems," Complexity, Hindawi, vol. 2020, pages 1-15, January.
    3. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    4. 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.
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    Cited by:

    1. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    2. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.

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