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

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

A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain (0,lπ) with l>0 is considered. According to the normal form method and the center manifold theorem for reaction-diffusion equations, the explicit formulas deter...

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Main Authors: Cun-Hua Zhang, Xiang-Ping Yan
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2015/657307
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spelling doaj-7e40f5b4e4f0483e82956e04f2baee812020-11-24T21:04:03ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/657307657307Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary ConditionCun-Hua Zhang0Xiang-Ping Yan1Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaA reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain (0,lπ) 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.http://dx.doi.org/10.1155/2015/657307
collection DOAJ
language English
format Article
sources DOAJ
author Cun-Hua Zhang
Xiang-Ping Yan
spellingShingle Cun-Hua Zhang
Xiang-Ping Yan
Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
Journal of Applied Mathematics
author_facet Cun-Hua Zhang
Xiang-Ping Yan
author_sort Cun-Hua Zhang
title Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
title_short Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
title_full Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
title_fullStr Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
title_full_unstemmed Normal Forms of Hopf Bifurcation for a Reaction-Diffusion System Subject to Neumann Boundary Condition
title_sort normal forms of hopf bifurcation for a reaction-diffusion system subject to neumann boundary condition
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2015-01-01
description A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain (0,lπ) 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.
url http://dx.doi.org/10.1155/2015/657307
work_keys_str_mv AT cunhuazhang normalformsofhopfbifurcationforareactiondiffusionsystemsubjecttoneumannboundarycondition
AT xiangpingyan normalformsofhopfbifurcationforareactiondiffusionsystemsubjecttoneumannboundarycondition
_version_ 1716772233126346752

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