Abstract:

sing the continuation theorem based on coincidence degree theory, we studied the existence of positive periodic solutions for a predatorprey system with infinite delay and nonmonotonic functional response. Two bounded open sets were obtained by means of analytic technique and a set of sufficient conditions for this system to have at least two positive periodic solutions was also obtained. It was revealed that when the carrying capacity of prey species and the increasing rate of predator species are all sufficiently large, the system will bring periodic oscillation of biological nature.

Key words: predatorprey system, nonmonotonic functional response, multiple periodic solution, coincidence degree