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

Ruyuan Zhang

doi:10.3934/cpaa.2005.4.445

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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

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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.

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

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