Time-reversible and equivariant pitchfork bifurcation

In this note we describe a new phenomenon in steady-state bifurcations of time-reversible and equivariant vector fields. When the eigenspace associated with a pair of imaginary eigenvalues that passes through zero onto the real line is separable from the nullspace associated with the fixed zeros of...

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Bibliographic Details
Published in:Physica. D 1998, Vol.112 (1), p.117-121
Main Authors: Lim, Chjan C., McComb, I-Heng
Format: Article
Language:English
Subjects:
Equivariant bifurcations
Pitchfork bifurcation
Stability
Time-reversible
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Summary:In this note we describe a new phenomenon in steady-state bifurcations of time-reversible and equivariant vector fields. When the eigenspace associated with a pair of imaginary eigenvalues that passes through zero onto the real line is separable from the nullspace associated with the fixed zeros of the spectrum, we prove that a pitchfork bifurcation occurs.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(97)00205-4