一类具有Watt型功能性反应的捕食系统的极限环与稳定性

The Stability and Limit Cycles of a Class Predator-prey System with Watt Type Functional Response

研究一类具有Watt型功能性反应的捕食模型.讨论了该系统正平衡点的存在性以及非负平衡点的性态,应用Poincare-Bendixson定理和张芷芬定理,证明了极限环的存在性和唯一性,并采用构造Dulac函数的方法,获得了正平衡点全局渐近稳定性的一个充分条件.

A class of predator prey model with Watt type functional response is studied. The existence of positive equilibrium point and the properties of non-negative equilibrium points are discussed. It proves the existence and uniqueness of limit cycles applying the Poincare-Bendixson theorem and Zhang Zhifen theorem. With the methods of constructing Dulac function, it obtains an ample factor of positive equilibrium points global asymptotic stability.