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Journal of Applied Mathematics
Volume 2015, Article ID 657307, 12 pages
Research Article

Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition

Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 14 May 2015; Accepted 12 July 2015

Academic Editor: Alain Miranville

Copyright © 2015 Cun-Hua Zhang and Xiang-Ping Yan. 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.


A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain with is considered. According to the normal form method and the center manifold theorem for reaction-diffusion equations, the explicit formulas determining the properties of Hopf bifurcation of spatially homogeneous and nonhomogeneous periodic solutions of system near the constant steady state are obtained.