泛函捕食者——食饵系统正周期解的全局存在性

Global Existence of Positive Periodic Solution of Periodic Predator — prey System with Functional Response

基于Gains and Mawhin的重合度延拓定理和泛函反应知识,证明了在一个周期环境中带有泛函反应的捕食者--食饵系统正周期解的全局存在性.该系统是具有2个捕食者x2,x3和2个食饵x1,x2的一条食物链.通过使用延拓定理和泛函知识,得到了一个关于该非自治系统的很好的结论.

With the help of a continue theorem based on Gains and Mawhins' coincidence degree and the knowledge of the Functional response, easily verifiable criteria are established for the global existence of positive periodic solution of a predator-prey system with functional response in a periodic environment. The system is a biological food chain which has two predators x_2,x_3 and two preys x_1,x_2. In the paper, the authors use the Gains and Mawhins' coincidence degree, and get a very good conclusion.