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Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect

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  • Han, Bingtao
  • Jiang, Daqing

Abstract

In this paper, we examine a stochastic prey-predator system with fear effect and general anti-predator behavior. To tackle the impact of stochastic perturbations, we first propose a p-stochastic threshold method to construct several necessary p-Lyapunov functions. Then by defining a quasi-carrying capacity x∗, sufficient conditions are established for the existence and uniqueness of stationary distribution ϖ⋅ of the system. By solving the Fokker-Planck equation, the approximate expression of probability density function of the distribution ϖ⋅ around its quasi-positive equilibrium is further derived. Besides, the extinction of prey and predator populations is studied. Finally, some numerical examples are provided to verify our theoretical results and study two aspects: (i) the impact of anti-predator behavior; (ii) the effect of prey fear.

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  • Han, Bingtao & Jiang, Daqing, 2022. "Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006683
    DOI: 10.1016/j.chaos.2022.112458
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    References listed on IDEAS

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    4. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
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    6. Wenxu Ning & Zhijun Liu & Lianwen Wang & Ronghua Tan, 2021. "Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1435-1459, December.
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    Cited by:

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    2. Cao, Nan & Fu, Xianlong, 2023. "Stationary distribution and extinction of a Lotka–Volterra model with distribute delay and nonlinear stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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