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Dynamics caused by the mean-reverting Ornstein–Uhlenbeck process in a stochastic predator–prey model with stage structure

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  • Mu, Xiaojie
  • Jiang, Daqing

Abstract

There are many species that go through different life stages in nature, they have different ecological characteristics in different stages, besides, stochastic variation exists in the natural environment. Based on this biological phenomenon, we develop and investigate dynamics in a predator–prey system with stage structure and the mean-reverting Ornstein–Uhlenbeck processes. We prove that this system satisfies the existence and uniqueness of globally positive equilibrium. The sufficient conditions for the existence of a stationary Markov process in stochastic system are attained. We deal with explicit expression and the existence of density function of the system which make a great contribution to biological intrinsic essence for the system. In addition, the sufficient criteria for extinction of the predator populations is derived. Finally, numerical simulations are furnished to illustrate the analysis results.

Suggested Citation

  • Mu, Xiaojie & Jiang, Daqing, 2024. "Dynamics caused by the mean-reverting Ornstein–Uhlenbeck process in a stochastic predator–prey model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077923013474
    DOI: 10.1016/j.chaos.2023.114445
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    References listed on IDEAS

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    1. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. 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).
    3. 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.
    4. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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