周期随机捕食-食饵系统的周期解的存在性

The Existence of Periodic Solution of Periodic Stochastic Predator-Prey Model

利用随机分析的方法,研究捕食者具有HollingⅡ增长函数的周期随机捕食-食饵系统的周期解的存在性。通过李雅普诺夫泛函方法证明,对于给定的任意正初始值,系统都存在唯一的全局正解。给出系统存在非平凡的正周期解的充分条件,得到系统持久性与灭绝的充分条件。最后,给出数值模拟来验证主要结果。

In this paper,the existence of periodic solutions for a periodic stochastic predator-prey model with HollingⅡgrowth function in the predator was studied by stochastic analysis.It was proved that the system had a unique global positive solution for any given positive initial value by the Lyapunov functional method.Then some sufficient conditions for the existence of nontrivial positive periodic solutions were given,and the persistence and extinction of the population were proved.Finally,some numerical simulations were given to verify the main results.