具有恒定容量避难所的 Filippov捕食者-食饵模型的全局动力学

Global Dynamics of a Filippov Predator-Prey Model with a Constant-Capacity Refuge

本文研究了一类具有恒定容量避难所的Filippov捕食者-食饵模型。 应用Filippov方法研究了模型的滑模动力学,并进一步研究了模型的全局动力学。 证明了系统存在唯一的正平衡,且该平衡是 全局渐近稳定的。结果表明,建立适当容量的避难所有利于维持捕食者与被捕食者之间的平衡。

In this paper, a predator-prey model with a constant-capacity refuge is studied. We apply Filippov method to study the sliding mode dynamics of the model, and studied the global dynamics furtherly. It is proved that there exists a unique equilibrium and the equilibrium is globally asymptotically stable. The results show that the estab- lishment of a refuge with appropriate capacity is beneficial to maintain the balance between predator and prey.