Phys. Rev. E 78, 036214 (2008) [4 pages]Local theory of the slanted homoclinic snaking bifurcation diagramReceived 8 February 2008; revised 24 August 2008; published 12 September 2008 Localized states in out of equilibrium one-dimensional systems are described by the homoclinic snaking associated with the infinite sequence of multibump localized solutions of the corresponding time reversible dynamical system. We show that when the pattern undergoes a saddle-node bifurcation the homoclinic snaking bifurcation diagram becomes slanted and a finite set of localized states continue to exist outside the region of bistability. This generic behavior offers a local theory resolution of the discrepancy between models and experiments. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.78.036214
DOI:
10.1103/PhysRevE.78.036214
PACS:
05.45.−a, 02.30.Oz, 89.75.Kd
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