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

Bingtao Han and Daqing Jiang

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

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.

Keywords: Stochastic prey-predator system; Nonlinear perturbation; Anti-predator behavior; Stationary distribution; Extinction; Density function (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006683

DOI: 10.1016/j.chaos.2022.112458

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