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A stochastic predator–prey system with modified LG-Holling type II functional response

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  • Chen, Xingzhi
  • Tian, Baodan
  • Xu, Xin
  • Zhang, Hailan
  • Li, Dong

Abstract

In this paper, a stochastic two-predator one-prey system with modified Leslie–Gower and Holling-type II functional response is proposed, which is randomly disturbed by the well-known mean-reverting Ornstein–Uhlenbeck process. By Itoˆ’s integral formula, stochastic comparison theorem, the strong law of large number theorem for martingales, and modeling and analysis methods in stochastic differential equations, the existence and uniqueness of the global positive solution for the system are discussed. Then, the additional conditions for the persistence in the mean and extinction of the system are obtained, respectively. Besides, the effects of the speed of reversion and the intensity of volatility in the Ornstein–Uhlenbeck process on the dynamics of the system are investigated. Furthermore, the ergodic stationary distribution of the system under a low-level intensity of stochastic noise is also derived, which indicates that x, y1 and y2 will be persist and fluctuate around the positive values. Finally, a series of numerical examples are provided to verify the correctness of the theoretical analysis.

Suggested Citation

  • Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:449-485
    DOI: 10.1016/j.matcom.2022.06.016
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    References listed on IDEAS

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