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  

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

作　　者：张雯雯 刘志军 王清龙 Zhang Wenwen;Liu Zhijun;Wang Qinglong(School of Mathematics and Statistics,Hubei Minzu University,Hubei Enshi 445000)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《数学物理学报（A辑）》2024年第5期1368-1379,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(12101211);湖北省自然科学基金(2023AFB1095)。

摘　　要：该文建立了一类具有Ornstein-Uhlenbeck过程、恐惧效应、Crowley-Martin型和修正的Leslie-Gower型功能反应函数的捕食者-食饵模型.首先通过构造合适的Lyapunov函数证明了全局解的存在唯一性,随后获得了两物种指数绝灭和平稳分布存在的充分条件.进一步通过求解相应的Fokker-Planck方程得到了概率密度函数的具体表达式.最后通过三个数值例子验证了理论结果的可行性,其研究表明随机干扰的波动强度和回复速率均会影响种群的生存.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 suficient 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.

关 键 词：捕食者-食饵模型 ORNSTEIN-UHLENBECK过程 指数绝灭 平稳分布 概率密度函数 

分 类 号：O175[理学—数学]