具有避难所和Ornstein-Uhlenbeck过程的随机三种群捕食模型的持久与灭绝

Persistence and Extinction of a Stochastic Three-population Predation Model with Refuge and Ornstein-Uhlenbeck Process

目前大多数的捕食模型都是用白噪声描述环境的随机性,针对真实情境下,模型中的参数可能满足Ornstein-Uhlenbeck过程的问题,提出具有避难所和Ornstein-Uhlenbeck过程的随机三种群捕食模型。利用伊藤公式、微分不等式及随机分析理论对模型进行动力学行为分析。证明了模型全局正解的存在唯一性,分别得到了每个种群平均持久生存和灭绝的充分条件,最后利用python进行数值模拟,验证了定理中所得到的结论,并进一步研究了避难所对种群数量的影响。

Most current predation models describe the stochastic nature of the environment in terms of white noise,for the problem that the parameters in the model may satisfy the Ornstein-Uhlenbeck process in a real situation,a stochastic three-species predation model with refuge and Ornstein-Uhlenbeck process is proposed.The dynamic behavior of the model is analyzed by its formula,differential inequality and stochastic analysis theory.The existence and uniqueness of the global positive solution of the model are proved,sufficient conditions for the average persistence and extinction of each population were obtained separately,finally,python is used to carry out numerical simulation to verify the conclusions obtained in the theorem,and further study the impact of refuge on population size.