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Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects. (English) Zbl 1181.37119

Summary: This paper is concerned with a delayed predator-prey diffusive system with Neumann boundary conditions. The bifurcation analysis of the model shows that Hopf bifurcation can occur by regarding the delay as the bifurcation parameter. In addition, the direction of Hopf bifurcation and the stability of bifurcated periodic solution are also discussed by employing the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs). Finally, the effect of the diffusion on bifurcated periodic solution is considered.

MSC:

37N25 Dynamical systems in biology
92D25 Population dynamics (general)
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
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