具有恐惧效应和Allee效应的合作捕食系统的稳定性分析

Stability Analysis of Hunting Cooperation System with Fear Effect and Allee Effect

合作捕获是生物数学研究的重要内容,随着研究的深入,人们发现合作捕获不仅会对食饵产生Allee效应,还会对食饵产生恐惧效应。对由合作捕食对食饵同时产生恐惧效应和Allee效应的捕获系统进行研究,根据笛卡尔定理得到了平衡点存在的条件及平衡点的稳定性,通过Matlab数值模拟验证了当捕食者合作捕获对食饵同时产生恐惧效应和Allee效应时,捕食者-食饵系统存在食饵与捕食者共存的情况,这样不仅保留了生物物种的多样性,而且保护了生态系统的稳定性。

Hunting cooperation predator system is an important research content of biological mathematics.With the deepening of research,people have discovered that the system not only produces an Allee effect,but also produces a fear effect on the prey.This paper studies the fear effect and the Allee effect of prey for the hunting cooperation predator system.The parameter conditions for the existence of equilibrium points are obtained by Descartes’theorem,and the stability of the equilibrium points is discussed.The conclusion is verified by Matlab numerical simulation.It is verified that when the fear effect and the Allee effect of prey,the system coexists with prey and the predator,which not only preserves the diversity of biological species,but also protects the stability of the ecosystem.