Existence of Periodic Solutions of Predator-Prey Diffusive System with Ratio-Dependence III Type and Stage Structure

In this paper, a non-autonomous predator-prey system with Ratio-Dependence III type functional response and stage structure for predator and time delay in patch circumstances is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained. Some new results are obtained.