Multiple positive periodic solutions of a delayed discrete predator–prey system with type IV functional responses

In this paper, a discrete periodic predator–prey system with type IV functional responses and time delay is investigated. Using Gaines and Mawhin’s continuation theorem from coincidence degree theory as well as some prior estimates, we get sufficient conditions for the existence of positive periodic solutions of the system. This is also the first time that the coincidence degree theory has been used to obtain multiple positive periodic solutions in discrete ecological systems.