基于比率且包含食饵避难的Holling-Tanner模型分析

Analysis of a Holling-Tanner model with ratio-dependence incorporating a prey refuge

考虑了一个基于比率且包含食饵避难的Holling-Tanner模型。分析了系统平衡点存在和局部渐近稳定性,并构造Lyapunov函数证明了正平衡点的全局渐近稳定性。利用分岔理论,发现系统在正平衡点经历了Hopf分岔,且出现了惟一的极限环。

A Holling-Tanner model with ratio-dependence incorporating a prey refuge was discussed. The existence and local asymptotic stability of the equilibria of the system were analyzed, and global asymptotic stability of the positive equilihrium was proved by constructing the Lyapunov function. By using bifurcation theory, it was shown that the system exporienees Hopf bifurcation at positive equicibrium, and the uniqueness of the limit cycle of the system was found.