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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.

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