Scaling laws for bubbling bifurcations

Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2009) Scaling laws for bubbling bifurcations. Nonlinearity, 22 11: 2607-2631. doi:10.1088/0951-7715/22/11/002

Author Gonzalez-Tokman, Cecilia
Hunt, Brian R.
Title Scaling laws for bubbling bifurcations
Journal name Nonlinearity   Check publisher's open access policy
ISSN 0951-7715
Publication date 2009
Year available 2009
Sub-type Article (original research)
DOI 10.1088/0951-7715/22/11/002
Open Access Status
Volume 22
Issue 11
Start page 2607
End page 2631
Total pages 25
Place of publication Temple Way, Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Abstract We establish rigorous scaling laws for the average bursting time for bubbling bifurcations of an invariant manifold, assuming the dynamics within the manifold to be uniformly hyperbolic. This type of global bifurcation appears in nearly synchronized systems, and is conjectured to be typical among those breaking the invariance of an asymptotically stable hyperbolic invariant manifold. We consider bubbling precipitated by generic bifurcations of a fixed point in both symmetric and non-symmetric systems with a codimension one invariant manifold, and discuss their extension to bifurcations of periodic points. We also discuss generalizations to invariant manifolds with higher codimension, and to systems with random noise.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Created: Thu, 30 Apr 2015, 10:23:53 EST by Kay Mackie on behalf of School of Mathematics & Physics