Multiperiodicity to a Certain Delayed Predator-Prey Model

The delayed predator-prey system with generalized non-monotonic functional responses and stage structure was investigated in the present paper. By virtue of Mawhin's coincidence degree and the application of inequalities technique, we are successful to generate some novel conditions to guarantee that the system has at least two positive periodic solutions. It is shown that all parameters of the system have effects on the existence of positive periodic solutions and the period of the coefficients can also affect the existence of positive periodic solutions. In the end, an illustrative example is presented to the feasibility of the main results.