Phase-space structure of two-dimensional excitable localized structures

Details Phase-space structure of two-dimensional excitable localized structures Phase-space structure of two-dimensional excitable localized structures

2007-03-07

arxiv.org/abs/nlin/0703011v1

Phys. Rev. E 75, 026217 (2007)

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 9 figures

Scientific paper

10.1103/PhysRevE.75.026217

In 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 bifurcation leads to an 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.

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