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Dynamics Analysis of a Stochastic Leslie–Gower Predator-Prey Model with Feedback Controls

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  • Huailan Ren
  • Wencai Zhao

Abstract

This study focuses on the investigation of a stochastic Leslie–Gower predator-prey model with feedback controls and Holling type II functional responses. First, the existence and uniqueness of a global positive solution to the system under white noise interference are proved. Second, the conditions for the existence of the system’s positive recurrence are established by constructing suitable Lyapunov functions. Additionally, the persistence and extinction of prey and predator in the system are discussed, and the impacts of noise interference and feedback controls on the system are revealed. Finally, we validate the theoretical results by numerical simulations.

Suggested Citation

  • Huailan Ren & Wencai Zhao, 2019. "Dynamics Analysis of a Stochastic Leslie–Gower Predator-Prey Model with Feedback Controls," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-13, December.
    • Handle: RePEc:hin:jnlmpe:8631272
    DOI: 10.1155/2019/8631272
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