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Phase-space structure of two-dimensional excitable localized structures

AutorGomila, Damià ; Jacobo, Adrián ; Matías, Manuel A. ; Colet, Pere
Palabras claveOptical Kerr effect
Optical solitons
Fecha de publicación28-feb-2007
EditorAmerican Physical Society
CitaciónPhysical Review E 75, 026217 (2007)
ResumenIn this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the instability leads to a excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.
Descripción10 pages.-- PACS numbers: 05.45.-a, 42.65.Sf, 89.75.Fb.-- ArXiv pre-print: http://arxiv.org/abs/nlin.PS/0703011.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.75.026217.
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