2007/02/28 by Damia Gomila, Damià Gomila, Adrián Jacobo +4 · 2 citations
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #math.DS #nlin.PS #physics.optics #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.75.026217
published as Phys. Rev. E 75, 026217 (2007) · 10 pages, 9 figures
openalex publication_date 2007/02/28 · arxiv created 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.