具有合作捕食与种内竞争的一类捕食者–食饵模型的Hopf分支

Hopf Bifurcation of a Predator-Prey System with Cooperative Hunting and Intraspecific Competition

本文研究了一类具有合作捕食和种内竞争的捕食者–食饵模型。该模型的参数空间被划分为几个不同的区域,在每个参数区域,研究了系统的动力学行为,包括内平衡点的个数、稳定性和Hopf分支。结果表明该模型会发生两次Hopf分支。分别与没有合作捕食和不存在种内竞争的捕食者–食饵模型进行比较,指出Hopf分支的发生是由合作捕食引起的,而两次Hopf分支是由种内竞争引起的。

We consider a predator-prey model with cooperative hunting and intraspecific competition in predators. The parameter space of the model is divided into several mutually exclusive regions. In each region, the dynamics of the system is investigated, including the number of interior equilibria, stability and Hopf bifurcation. It is presented that Hopf bifurcation may occur twice. By comparing to the dynamics of the systems without cooperative hunting and without the intraspecific competi-tion in predators, respectively, it is shown that the occurrence of Hopf bifurcation is caused by in-traspecific competition.