具有连续时滞和功能性反应的非自治竞争系统的持续生存

Persistence of Nonautonomous Competition System with Continuous Time Delay and Functional Responce

本文利用Lyapunov-Razumikhin理论讨论了具有连续时滞和类功能性反应的非自治扩散竞争系统.此系统有两个种群n个斑块,其中一个种群可以在n个斑块中自由扩散,另一种群被限定在一斑块中不能扩散.当系数满足一定的条件时,证明了系统是持续生存的,此外,给出了该系统的一周期解全局吸引的充分条件.

In this paper, a nonautonomous diffusion competition system with continuous time delay and I type functional response is studied by employing the Lyapunov-Razumikhin technique. There are two species and n patches in the system, one of the two species can diffuse between n patches, and the other is confined to one patch. It is proved that the system can be persistent under some conditions. Furthermore, sufficient conditions are established for global attractivity of a periodic solution of the system.