一类具有恐惧和合作狩猎捕食系统的全局分析

Global analysis of a predator-prey system with fear effect and hunting cooperation

为研究食饵对捕食者的恐惧、捕食者之间的合作狩猎以及环境因素对物种数量的影响,建立一个具有恐惧效应和合作狩猎行为的Leslie-Gower捕食者-食饵模型。利用微分方程比较原理证明了解的有界性,使用重合度理论的方法分析了周期解存在的条件,通过构造Lyapunov函数分析了周期解的全局吸引性。利用Matlab进行数值模拟,验证了理论结果。

In order to study the effects of the predator′s fear effect,hunting cooperation between predators,and environmental factors on the number of prey and predator,this paper established a Leslie-Gower predator-prey model with fear effect and hunting cooperation.The boundedness of the solutions is proved by the comparison theorem of differential equations,and the conditions for the existence of periodic solutions are given by coincidence degree theorem,and the global attractivity of the periodic solution is analyzed by constructing a Lyapunov function.Numerical simulations are performed through matlab to verify the theoretical results.