Stochastic Resonance in an Extended FitzHugh-Nagumo System: the Role of Selective Coupling

We analyze several aspects of the phenomenon of stochastic resonance in reaction-diffusion systems, exploiting the nonequilibrium potential's framework. The generalization of this formalism (sketched in the appendix) to extended systems is first carried out in the context of a simplified scalar model, for which stationary patterns can be found analytically. We first show how system-size stochastic resonance arises naturally in this framework, and then how the phenomenon of ar...

Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using "nonequilibrium potential" techniques. We now consider a field-dependent diffusivity and show that the "selectivity" of the coupling is more efficient for achieving stochastic-resonance enhancement than its overall value in the constant-diffusivity ca...

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to oth...

Previous works have shown numerically that the response of a ``stochastic resonator'' is enhanced as a consequence of spatial coupling. Also, similar results have been obtained in a reaction-diffusion model by studying the phenomenon of stochastic resonance (SR) in spatially extended systems using "nonequilibrium potential" (NEP) techniques. The knowledge of the NEP for such systems allows us to determine the probability for the decay of the metastable extended states, and ap...

We consider the coaction of two distinct noise sources on the activation process of a single and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to sce...

Using a model of the FitzHugh-Nagumo oscillator in the excitable regime, we investigate the influence of the L\'evy noise's properties on the effect of coherence resonance. In particular, we demonstrate that the L\'evy noise can be a constructive or destructive factor providing for enhancement or suppression of noise-induced coherence. We show that the positive or negative role of the L\'evy noise impact is dictated by the noise's stability index and skewness parameter. The c...

Noise is ubiquitous in various systems. In systems with multiple timescales, noise can induce various coherent behaviors. Self-induced stochastic resonance (SISR) is a typical noise-induced phenomenon identified in such systems, wherein noise acting on the fast subsystem causes stochastic resonancelike boundary crossings. In this paper, we analyze the stochastic periodic orbits caused by SISR in fast-slow systems. By introducing the notion of the mean first passage velocity t...

We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic dynamics such as frequency synchronization and phase synchronization, where the degree of synchronization can be quantified by the ratio of the interspike interval of the two excitable neural populations and the phase synchronization index, respec...

We systematically investigate the phenomena of coherence resonance in time-delay coupled networks of FitzHugh-Nagumo elements in the excitable regime. Using numerical simulations, we examine the interplay of noise, time-delayed coupling and network topology in the generation of coherence resonance. In the deterministic case, we show that the delay-induced dynamics is independent of the number of nearest neighbors and the system size. In the presence of noise, we demonstrate t...

The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous studies, in which extreme events (EE) were observed solely in coupled FHN oscillators, we demonstrate that a single system can exhibit EE induced by noise. Perturbation of the deterministic model in its steady state by random fluctuations re...