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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/657307 |
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| _version_ | 1850214296884084736 |
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| author | Cun-Hua Zhang Xiang-Ping Yan |
| author_facet | Cun-Hua Zhang Xiang-Ping Yan |
| author_sort | Cun-Hua Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-7e40f5b4e4f0483e82956e04f2baee81 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7e40f5b4e4f0483e82956e04f2baee812025-08-20T02:08:57ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2015/657307 |
| work_keys_str_mv | AT cunhuazhang normalformsofhopfbifurcationforareactiondiffusionsystemsubjecttoneumannboundarycondition AT xiangpingyan normalformsofhopfbifurcationforareactiondiffusionsystemsubjecttoneumannboundarycondition |