Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction–diffusion model
In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction–diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclu...
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| Published in | Nonlinear analysis: real world applications Vol. 13; no. 4; pp. 1961 - 1977 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.2012
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| Online Access | Get full text |
| ISSN | 1468-1218 1878-5719 |
| DOI | 10.1016/j.nonrwa.2012.01.001 |
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| Abstract | In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction–diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclude that the spatially homogeneous periodic solutions are locally asymptotically stable and the spatially heterogeneous periodic solutions are unstable. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results. |
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| AbstractList | In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction–diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclude that the spatially homogeneous periodic solutions are locally asymptotically stable and the spatially heterogeneous periodic solutions are unstable. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results. |
| Author | Xu, Chuang Wei, Junjie |
| Author_xml | – sequence: 1 givenname: Chuang surname: Xu fullname: Xu, Chuang organization: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China – sequence: 2 givenname: Junjie surname: Wei fullname: Wei, Junjie email: weijj@hit.edu.cn, Weijj1954@yahoo.com organization: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China |
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| Keywords | Spatially homogeneous periodic solution Schnakenberg reaction–diffusion model Hopf bifurcation Spatially heterogeneous periodic solution |
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| SubjectTerms | Asymptotic properties Boundary conditions Hopf bifurcation Mathematical models Nonlinearity Schnakenberg reaction–diffusion model Spatially heterogeneous periodic solution Spatially homogeneous periodic solution |
| Title | Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction–diffusion model |
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