Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems

TL;DR

This paper investigates how noise influences the collective behavior of coupled FitzHugh-Nagumo oscillators, revealing transitions from steady states to oscillations and chaos, and provides a theoretical framework matching simulations.

Contribution

It introduces a cumulant expansion approach to analyze noise-induced dynamics in large ensembles of coupled excitable systems, bridging stochastic simulations and bifurcation analysis.

Findings

Noise causes transitions from equilibrium to oscillations and chaos.

The cumulant expansion accurately predicts bifurcation scenarios.

Large ensembles exhibit diverse collective behaviors depending on noise intensity.

Abstract

We study stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. Diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed in the course of this transition. In order to understand details and mechanisms of noise-induced dynamics we consider a thermodynamic limit $N\to\infty$ of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In the Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.