Periodic solutions in a delayed predator-prey models with nonmonotonic functional response

Wan-Tong Li; Yong-Hong Fan

doi:10.3934/dcdsb.2007.8.175

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2007, Volume 8, Issue 1: 175-185. Doi: 10.3934/dcdsb.2007.8.175

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Periodic solutions in a delayed predator-prey models with nonmonotonic functional response

Wan-Tong Li^1, and
Yong-Hong Fan²

1.
School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematics and Information Sciences, Ludong University, Yantai, Shandong 264025

Received: September 30, 2006

Revised: October 31, 2006

Published: December 2006

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Abstract

By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a delayed predator-prey model with nonmonotonic functional response ${ x^{'}(t)=x(t)[ a(t)-b(t)x(t)] -\frac{x(t)y(t)}{m^2+x^2(t)},$
$y^{'}(t)=y(t)[ \frac{\mu (t)x(t-\tau )}{m^2+x^2(t-\tau )} -d(t)]. \]$ is established, where $a(t), b(t), \mu (t)$ and $d(t)$ are all positive periodic continuous functions with period $\omega >0$, $m>0$ and $\tau \geq 0 $ are constants.

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Mathematics Subject Classification: Primary: 34K15, 34C25 Secondary: 92D25.

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