考虑多个避难所中的捕食-食饵快慢动力学分析

Fast and Slow Predator-Prey Dynamics with Multiple Refuges

基于实际生态现象,考虑被捕食者会有多个避难所的情形,建立了一个多个避难所的捕食-食饵模型.基于不同的时间尺度,运用奇异摄动理论分析慢系统的动力学行为.稳定性分析得出当阈值条件大于1时,会有Hopf分支现象出现.结果表明,避难所的添加可能会导致系统失去稳定性.另外,对被捕食者有一个避难所和多个避难所这两种情况进行了比较,发现被捕食者在公开区域和避难所之间的移动,以及避难所的大小也会影响捕食-食饵动力学性态.

In this paper we established a predator-prey model with multiple refuges for prey. Based on two different time scales, applying the singular perturbation techniques we analyse the dynamics on the slow system. The stability analyses are performed and Hopf bifurcation occurs when the threshold condition is greater than one value. It is shown that adding refuges for prey may lead to stability lost. Furthermore, the case of one refuge and multiple refuges are compared. It is found that the migration of prey among patches affects the dynamics of predator-prey system. The effect of the migration between open habitat and refuges is stronger than that of the migration among refuges for prey. The refuge size also infects the dynamics of predator-prey system.