American Institute of Mathematical Sciences

July  2007, 8(1): 175-185. doi: 10.3934/dcdsb.2007.8.175

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

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

Received  October 2006 Revised  November 2006 Published  April 2007

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.
Citation: Wan-Tong Li, Yong-Hong Fan. Periodic solutions in a delayed predator-prey models with nonmonotonic functional response. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 175-185. doi: 10.3934/dcdsb.2007.8.175
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