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Zbl 1172.34043
Fan, Yong-Hong; Wang, Lin-Lin
Periodic solutions in a delayed predator-prey model with nonmonotonic functional response.
(English)
[J] Nonlinear Anal., Real World Appl. 10, No. 5, 3275-3284 (2009). ISSN 1468-1218

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 \align 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)), \endalign 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 2000:
*34K13 Periodic solutions of functional differential equations
92D25 Population dynamics
47N20 Appl. of operator theory to differential and integral equations

Keywords: predator-prey model; nonmonotonic functional response; positive periodic solution; coincidence degree

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