Please use this identifier to cite or link to this item:
Title: Cocoon bifurcation in three-dimensional reversible vector fields
Authors: DUMORTIER, Freddy 
IBANEZ MESA, Santiago 
Kobubu, H.
Issue Date: 2006
Publisher: Institute Of Physics
Source: NONLINEARITY, 19(2). p. 305-328
Abstract: The cocoon bifurcation is a set of rich bifurcation phenomena numerically observed by Lau (1992 Int. J. Bifurc. Chaos 2 543-58) in the Michelson system, a three-dimensional ODE system describing travelling waves of the Kuramoto-Sivashinsky equation. In this paper, we present an organizing centre of the principal part of the cocoon bifurcation in more general terms in the setting of reversible vector fields on R-3. We prove that in a generic unfolding of an organizing centre called the cusp-transverse heteroclinic chain, there is a cascade of heteroclinic bifurcations with an increasing length close to the organizing Centre, which resembles the principal part of the cocoon bifurcation. We also study a heteroclinic cycle called the reversible Bykov cycle. Such a cycle is believed to occur in the Michelson system, as well as in a model equation of a Josephson Junction (van den Berg et al 2003 Nonlinearity 16 707-17). We conjecture that a reversible Bykov cycle is, in its unfolding, an accumulation point of a sequence of cusp-transverse heteroclinic chains. As a first result in this direction, we show that a reversible Bykov cycle is an accumulation point of reversible generic saddle-node bifurcations of periodic orbits, the main ingredient of the cusp-transverse heteroclinic chain.
Document URI:
ISSN: 0951-7715
e-ISSN: 1361-6544
DOI: 10.1088/0951-7715/19/2/004
ISI #: 000235461400004
Category: A1
Type: Journal Contribution
Validations: ecoom 2007
Appears in Collections:Research publications

Show full item record

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.