Conditions for Global Attractivity of n-Patches Predator Prey Dispersion-Delay Models1

In this paper, a nonautonomous predator prey dispersion model with functional response and continuous time delay is studied, where all parameters are time dependent. In this system, which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rate effect. Furthermore, the sufficient conditions are established for global attractivity of a periodic solution of the system.