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Multiple periodic solutions of delayed predator–prey systems with type IV functional responses. (English) Zbl 1066.92050

Summary: We considered a periodic predator-prey system with type IV functional response, which incorporates the periodicity of the environment. Sufficient conditions for the existence of multiple positive periodic solutions are established by applying the continuation theorem. This is the first time that multiple periodic solutions are obtained by using the theory of coincidence degree. Moreover, unlike other types of functional responses, a type IV functional response declines at high prey densities. Thus the existing arguments for obtaining bounds of solutions to the operator equation \(Lx=\lambda Nx\) are inapplicable to our case and some new arguments are employed for the first time.

MSC:

92D40 Ecology
34K13 Periodic solutions to functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
37N25 Dynamical systems in biology
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References:

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