Multiple periodic solutions of a ratio-dependent predator–prey model

A delayed ratio-dependent predator–prey model with non-monotone functional response is investigated in this paper. Some new and interesting sufficient conditions are obtained for the global existence of multiple positive periodic solutions of the ratio-dependent model. Our method is based on Mawhin’s coincidence degree and some estimation techniques for the a priori bounds of unknown solutions to the equation Lx = λNx. An example is represented to illustrate the feasibility of our main result.