PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.