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Periodic solution for a stochastic non-autonomous competitive Lotka–Volterra model in a polluted environment

Author

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  • Jiang, Daqing
  • Zhang, Qiumei
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we consider a stochastic non-autonomous competitive Lotka–Volterra model in a polluted environment. We derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions. Furthermore, we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution. Finally we make simulations to illustrate our analytical results.

Suggested Citation

  • Jiang, Daqing & Zhang, Qiumei & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Periodic solution for a stochastic non-autonomous competitive Lotka–Volterra model in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 276-287.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:276-287
    DOI: 10.1016/j.physa.2016.12.008
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    References listed on IDEAS

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    1. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    2. Han, Qixing & Jiang, Daqing, 2015. "Periodic solution for stochastic non-autonomous multispecies Lotka–Volterra mutualism type ecosystem," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 204-217.
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    Cited by:

    1. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.
    2. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    3. Wang, Yuanshi, 2018. "Global dynamics of a competition–parasitism–mutualism model characterizing plant–pollinator–robber interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 26-41.
    4. Yuxiao Zhao & Linshan Wang & Yangfan Wang, 2021. "The Periodic Solutions to a Stochastic Two-Prey One-Predator Population Model with Impulsive Perturbations in a Polluted Environment," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 859-872, September.

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