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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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    1. Sharma, Swarnali & Samanta, G.P., 2015. "A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 69-84.
    2. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    3. Amirabad, H. Qolizadeh & RabieiMotlagh, O. & MohammadiNejad, H.M., 2019. "Permanency in predator–prey models of Leslie type with ratio-dependent simplified Holling type-IV functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 63-76.
    4. Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    5. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    7. Li, Shangzhi & Guo, Shangjiang, 2021. "Permanence of a stochastic prey–predator model with a general functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 308-336.
    8. Xu, Dongsheng & Liu, Ming & Xu, Xiaofeng, 2020. "Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    9. Lu, Chun, 2021. "Dynamics of a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 316-332.
    10. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
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