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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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