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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 547425, 5 pages
http://dx.doi.org/10.1155/2013/547425
Research Article

Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Mathematics, Liaoning Normal University, Dalian 116029, China
3School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China

Received 7 March 2013; Accepted 23 August 2013

Academic Editor: L. Jódar

Copyright © 2013 Zhenhua Bao and He Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. And all these oscillatory patterns are proved to be unstable.