一类具有 Ornstein-Uhlenbeck 过程的随机捕食者-食饵模型的指数绝灭、平稳分布和概率密度函数

Abstract

Abstract:

In the paper, a stochastic predator-prey model with Ornstein-Uhlenbeck process, fear effect, Crowley-Martin type and Leslie-Gower type functional responses is considered. Firstly, by constructing suitable Lyapunov functions, we prove that the existence and uniqueness of the global solution, and the sufficient conditions for the exponential extinction and the existence of stationary distribution are obtained. Secondly, we get access to the specific expression of probability density function via dealing with the corresponding Fokker-Planck equation. Finally, our theoretical results are verified by three numerical examples. The results show that the intensity of volatility and the reversion speed of stochastic disturbance will affect the survival of species.

Key words: Predator-Prey model, Ornstein-Uhlenbeck process, Exponential extinction, Stationary distribution, Probability density function

CLC Number:

O175

Zhang Wenwen, Liu Zhijun, Wang Qinglong. Exponential Extinction, Stationary Distribution and Probability Density Function of A Stochastic Predator-Prey Model with Ornstein-Uhlenbeck Process[J].Acta mathematica scientia,Series A, 2024, 44(5): 1368-1379.

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Exponential Extinction, Stationary Distribution and Probability Density Function of A Stochastic Predator-Prey Model with Ornstein-Uhlenbeck Process

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