Global stability and bifurcation analysis of a delayed predator-prey system with prey immigration

Electronic Journal of Qualitative Theory of Differential Equations

Junjie Wei¹  Gang Zhu² 

[1] Harbin Institute of Technology, Harbin, P. R. China;School of Education Science, Harbin University, Harbin, P.R. China ;

关键词: delay;    stability;    bifurcation;    center manifold;    normal form;   

DOI  :  10.14232/ejqtde.2016.1.13

来源: DOAJ

【 摘 要 】

A delayed predator-prey system with a constant rate immigration is considered. Local and global stability of the equilibria are studied, a fixed point bifurcation appears near the boundary equilibrium and Hopf bifurcation occurs near the positive equilibrium when the time delay passes some critical values. We also show the existence of the global Hopf bifurcation, and the properties of the fixed point bifurcation and the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem.

【 授权许可】

Unknown