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Periodic solutions in a delayed predator-prey model with nonmonotonic functional response. (English) Zbl 1172.34043

Summary: By using the continuation theorem of coincidence degree theory and some functional analytic techniques, several existence criteria are established for positive periodic solutions of a delayed predator-prey model with nonmonotonic functional response of the form

x ' (t)=x(t)(a(t)-b(t)x(t))-g(x(t))y(t),y ' (t)=y(t)(μ(t)g(x(t-τ))-d(t)),

where a(t), b(t), μ(t) and d(t) are all positive periodic continuous functions with period ω>0, τ is a nonnegative constant and g is a nonmonotonic functional response function. And an example is given to illustrate our main result.

MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
47N20Applications of operator theory to differential and integral equations