Bogdanov-Takens bifurcation for a diffusive predator-prey system with nonlocal effect and prey refuge. (English) Zbl 1510.35037
In this paper, some existence conditions of Turing bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation and Turing-Turing bifurcation are obtained for a diffusive predator-prey system with nonlocal effect and prey refuge subjects to the homogeneous Neumann boundary condition. The spatiotemporal dynamics near the Bogdanov-Takens bifurcation point is analyzed by utilizing the normal form theory. Some numerical simulations are provided to support the theory analysis.
Reviewer: Shangjiang Guo (Changsha)
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 35R09 | Integro-partial differential equations |
| 37L10 | Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems |
| 92D25 | Population dynamics (general) |
Keywords:
nonlocal effect; prey refuge; Bogdanov-Takens bifurcation; Turing bifurcation; Hopf bifurcation; Turing-Turing bifurcation; normal formReferences:
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