Noise induced extreme events in single Fitzhugh-Nagumo oscillator

TL;DR

This paper demonstrates that a single FitzHugh-Nagumo neuron model can exhibit noise-induced extreme events and bursting phenomena, expanding understanding of neuronal dynamics under stochastic influences.

Contribution

It reveals for the first time that a solitary FHN oscillator can produce extreme events due to noise, previously observed only in coupled systems.

Findings

Noise induces large-amplitude oscillations at low intensities.

Bursting phenomena are characterized by inter-spike interval statistics.

High noise levels lead to frequent large-amplitude oscillations via stochastic resonance.

Abstract

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 reveals the emergence of subthreshold/small-amplitude oscillations (SAO), eventually leading to rare and extreme large-amplitude oscillations (LAO), which become particularly evident at minimal noise intensities. We elucidate the route by which these EE emerge, confirming their occurrence through probability calculations of trajectories in phase space. Additionally, our investigation reveals bursting phenomena in the system, which are characterized by specific levels of noise amplitude and elucidated using inter-spike interval statistics. At higher noise amplitudes, frequent LAO production is observed and attributed to self-induced stochastic resonance. The emergence of EE is explained through the theory of large fluctuations, with the escape rates of trajectories estimated via both analytical and numerical approaches. This study is significant because it reveals EE and bursting phenomena in a single FHN oscillator, offering potential new insights into the dynamics of neuronal populations.