Journal of Applied Mathematics

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

Cun-Hua Zhang and Xiang-Ping Yan

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Abstract

A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain ( 0 , l π ) with l > 0 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 ( 0,0 ) are obtained.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 657307, 12 pages.

Dates
First available in Project Euclid: 17 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1439816422

Digital Object Identifier
doi:10.1155/2015/657307

Mathematical Reviews number (MathSciNet)
MR3384375

Citation

Zhang, Cun-Hua; Yan, Xiang-Ping. Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition. J. Appl. Math. 2015 (2015), Article ID 657307, 12 pages. doi:10.1155/2015/657307. https://projecteuclid.org/euclid.jam/1439816422


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