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Zbl 1181.37119
Hu, Guang-Ping; Li, Wan-Tong
Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 2, 819-826 (2010). ISSN 1468-1218

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 2000:: *37N25 Dynamical systems in biology
92D25 Population dynamics
37G40 Symmetries, equivariant bifurcation theory

Keywords: time delay; diffusion; normal form; Hopf bifurcation

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