随机环境下HollingⅢ型捕食-食饵系统动力学行为

Dynamical behaviors of the HollingⅢtype predator-prey model in a random environment

研究了由Markov链驱动的随机环境下HollingⅢ型捕食-食饵系统的动力学行为,应用随机Lyapunov分析、随机比较定理等方法证明了捕食-食饵系统的全局正解的存在唯一性,在此基础上研究了捕食者和食饵的随机最终上有界性,并且给出了食饵随机持久性的充分条件.

This work focus on dynamic behaviors of the predator-prey system with Markov switching.The main methods are Lyapunov function analysis,comparison theorem for stochastic differential equations,Fredholm alternative theorem,and constructing auxiliary stochastic processes etc.The existence and uniqueness of the global positive solution for the predator-prey system are obtained.Then bound of moments for the predator and prey and sufficient conditions for stochastic permanence of the prey are yielded.