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June  2005, 4(2): 445-461. doi: 10.3934/cpaa.2005.4.445

Hopf bifurcations of ODE systems along the singular direction in the parameter plane

Ruyuan Zhang 1,

1. 

Department of Mathematics Northeast Normal University, 130024 Changchun, Jilin

Received  March 2004 Revised  November 2004 Published  March 2005

This paper considers Hopf bifurcation of ordinary differential systems along the singular direction in the parameter plane. Hopf Bifurcation of the same system along non-singular directions have been studied recently in [9]. As an application of our main results, we also obtain results of existence and non-existence for a type of degenerate Hopf bifurcation (i.e., the type without transversality) for one parameter ODE systems.
Keywords: degenerate, central manifold, normal form, Hopf bifurcation, singular direction.
Mathematics Subject Classification: Primary82D10,76X05,35B60,35B4.
Citation: Ruyuan Zhang. Hopf bifurcations of ODE systems along the singular direction in the parameter plane. Communications on Pure and Applied Analysis, 2005, 4 (2) : 445-461. doi: 10.3934/cpaa.2005.4.445
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