一类加法Allee效应下的捕食-食饵系统的动力分析

Dynamic analysis of a predator-prey system with additive Allee effect

建立了一个食饵具有一个保护的区域和非保护区域的捕食-食饵模型.在考虑环境制约的情况下同时考虑了保护区的食饵具有加法Allee效应.根据食饵与捕食者的生物意义以及一些参数的快慢两个时间尺度,将系统分为快速系统和慢速系统.通过动力分析,给出了慢速系统平衡点的存在性、全局稳定性、Hopf分支以及极限环存在的条件,并通过数值分析及数值模拟加以验证.结果表明,Allee效应的存在改变了两物种的共存的条件,使系统动力行为更为复杂.

In this paper we establish a predator-prey model with a protection area and a open habitat for prey.Additive Allee effect in the prey of protection area and the environment carrying capacity of prey are considered.According to the biology of predator-prey system,fast and slow time scales are considered in some of the parameters.Based on two different time scales,the system is divided into a fast and a slow system.We analyze the dynamics of the slow system.Existence and global stability of equilibriums,existence of Hopf bifurcation and the limit cycle are performed.Combining mathematica analysis and numerical simulation,we verified the results above.The results show that the Allee effect change the conditions of the two species coexist.It makes the system dynamic behavior more complicated.