Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model. (English) Zbl 1257.35035
Summary: 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.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K58 | Semilinear parabolic equations |
Keywords:
spatially homogeneous periodic solution; spatially heterogeneous periodic solution; Neumann boundary conditionReferences:
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