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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
\begin{aligned} x'(t)&= x(t)(a(t)-b(t)x(t))- g(x(t))y(t),\\ y'(t)&= y(t)(\mu(t)g(x(t-\tau))-d(t)), \end{aligned}
where $$a(t)$$, $$b(t)$$, $$\mu(t)$$ and $$d(t)$$ are all positive periodic continuous functions with period $$\omega>0$$, $$\tau$$ is a nonnegative constant and $$g$$ is a nonmonotonic functional response function. And an example is given to illustrate our main result.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 92D25 Population dynamics (general) 47N20 Applications of operator theory to differential and integral equations
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