Stability and Hopf bifurcation in a Hutchinson model. (English) Zbl 1428.35034
Summary: In this paper we establish Hopf bifurcation phenomena for a diffusive Hutchinson model with delay effect and homogeneous boundary condition on a general open domain with a smooth boundary. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions via Lyapunov-Schmidt reduction.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K57 | Reaction-diffusion equations |
| 92D40 | Ecology |
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