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On the Existence of Periodic Solutions of a Three-Patch Diffusion Predator-Prey System

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On the Existence of Periodic Solutions of a Three-Patch Diffusion Predator-Prey System

Mohammed Ismaila, Atta A. K. Abu Hanyb, and Aysha Aghac

aDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

bDepartment of Mathematics, Faculty of Science, Al Azhar University of Gaza, Gaza, Via Israel

cDepartment of Mathematics, Faculty of Science, Al Aqsq University of Gaza, Via Israel Reprint requests to Atta Hany; E-mail: attahany@yahoo.com

Z. Naturforsch.64a,405 – 410 (2009); received March 18, 2008 / revised August 19, 2008

We establish a mathematical model for the three-patch diffusion predator-prey system with time delays. The theory of Hopf bifurcation is implemented, choosing the time delay parameter as a bifur- cation parameter. We present the condition for the existence of a periodic orbit of the Hopf-type from the positive equilibrium.

Key words:Predator-Prey Model; Time Delay; Diffusion; Hopf Bifurcation; Periodic Solutions.

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