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

Ruyuan Zhang

doi:10.3934/cpaa.2005.4.445

Article Contents

2005, Volume 4, Issue 2: 445-461. Doi: 10.3934/cpaa.2005.4.445

This issue Previous Article Global solvability for a singular nonlinear Maxwell's equations Next Article Asymptotic behavior of solutions to the nonlinear breakage equations

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: February 29, 2004

Revised: October 31, 2004

Published: May 2005

Abstract Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: Primary82D10,76X05,35B60,35B40.

Citation:

Article Metrics

HTML views() PDF downloads(48) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content