Abstract:

Using a continuation theorem based on Gaines and Mawhin’s coincidence degree, we studied the global existence of positive periodic solutions of a predatorprey diffusive system with mutual interference and ratio dependence. A set of easily verifiable sufficient conditions were obtained, which improved some known results. The results show  when the prey population intrinsic increasing rate is greater than the total consumption rate, the system will bring periodic oscillation of biological nature.

Key words: HollingTanner system, diffusive and mutual interference, coincidence degree theory, positive periodic solution