Front interaction induces excitable behavior

Abstract

Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Subthreshold perturbations decay exponentially. Superthreshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability.

Neuron-like spiking dynamics in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer

“…The presence of noise in any real experimental setup is unavoidable, and it could have interesting implications in the context of excitability. The interplay between noise and excitability has been studied in different contexts [29,43,44] and may randomly trigger excitable excursions, even for subthreshold perturbations. The emergence of oscillations due to the presence of noise is known as coherence resonance or internal stochastic resonance [43][44][45], and has been analyzed in detail in the context of noise-driven excitable systems [43].…”

“…In this context, excitable waves can emerge in extended systems which are locally excitable [7,25,26]. However, the spatial coupling can be responsible for the coherent structures emerging from the spiking dynamics even in systems that are non locally excitable [27,28], and for excitable-like behaviors which stem from front interactions [29]. Recent works have also focused on the characterization of travelling pulses in type-I excitable media [30,31].…”

Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability

“…Formula (24) suggests that the repetition rates θ d,c,s 0 are all proportional to the width of soliton ccomponents in the soliton-crystal structures Eqs. (19), (20) and (21), and inversely proportional to their amplitudes.…”

“…Although experiments have established unambiguously the possibility of several distinct soliton-lattice patterns in Kerr optical frequency-comb structures (see e.g. [25,24,26]), so far theoretical investigations of the mechanism of generation and stability of soliton combs in ring-shaped microresonators have focused mainly on patterns formed by spatial entanglement of bright solitons. The cases of solitoncomb structures composed of dark solitons, odd-polarity bright soliton lattice (i.e.…”

Neuronlike spiking dynamics in asymmetrically driven dissipative nonlinear photonic dimers

“…In this context, excitable waves can emerge in extended systems which are locally excitable [9,30,31]. However, the spatial coupling can be responsible for the coherent structures emerging from the spiking dynamics even in systems that are nonlocally excitable [32,33], and for excitablelike behaviors which stem from front interactions [34]. Recent works have also focused on the characterization of traveling pulses in type-I excitable media [35,36].…”