Positive periodic solutions for a generalized two-species semi-ratio-dependent predator–prey system in a two-patch environment

In this paper, we investigate a generalized two-species semi-ratio-dependent predator–prey system with the prey dispersal in a two-patch environment. With the help of a continuation theorem based on coincidence degree theory, we establish sufficient conditions for the existence of positive periodic solutions. Our results show that for any monotonic prey growth and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod–Haldane type, and the Beddington–DeAngelis type, the system always has at least one positive periodic solution.