一类被开发的捕食-食饵系统的定性分析

Qualitative Analysis of a Kind of Exploited Predator-Prey System

讨论了一类食饵种群被开发的两种群捕食系统,主要讨论了系统平衡点的行为以及系统的全局稳定性。用P ioncare切性曲线法及Du lac函数法得到了闭轨不存在的充分条件。用Hop f分支理论及张芷芬唯一性定理证明了极限环的存在唯一性。

A kind of predator-prey system is exploited. The paper mainly studied the behaviors of the equilibria and the stability. By constructing Dulac function and Pioncare curve, a sufficient condition of the nonexixtence of closed orbit was obtained. The existence and the uniquess of limit cycle which depend on Hopf bifurcation theory and unique theorem was proved.