Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model |
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| Authors: | Chuang Xu Junjie Wei |
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| Institution: | a Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, Chinab Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Alberta, Canada |
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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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| Keywords: | Schnakenberg reaction-diffusion model Hopf bifurcation Spatially homogeneous periodic solution Spatially heterogeneous periodic solution |
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