Excitability mediated by localized structures

Abstract

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.

4 pages, 5 figures; v2 minor changes + 1 new ref

References in corpus (2)

• Complex Patterns in a Simple System
• Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

Cited by in corpus (22)

• Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators
• Stability Analysis of the Lugiato-Lefever Model for Kerr Optical Frequency Combs. Part I: Case of Normal Dispersion
• Dark solitons in the Lugiato-Lefever equation with normal dispersion
• Observations of spatiotemporal instabilities in the strong-driving regime of an AC-driven nonlinear Schrödinger system
• Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures
• Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization
• Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
• Excitability in optical systems close to Z2-symmetry
• Influence of Stimulated Raman Scattering on Kerr domain walls and localized structures
• Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials
• Phase-space structure of two-dimensional excitable localized structures
• Logical operations with Localized Structures
• Dissipative soliton excitability induced by spatial inhomogeneities and drift
• Parametric localized patterns and breathers in dispersive quadratic cavities
• Effects of a localized beam on the dynamics of excitable cavity solitons
• Bifurcation structure of traveling pulses in Type-I excitable media
• Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
• Neuron-like spiking dynamics in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer
• Analytic Methods to Find Beating Transitions of Asymmetric Gaussian Beams in GNLS equations
• Front interaction induces excitable behavior
• Temporal localized structures in photonic crystal fiber resonators and their spontaneous symmetry breaking instability
• Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities