Mitigation of extreme events in an excitable system

TL;DR

This paper investigates a simple, easily implementable constant bias method to mitigate extreme events in coupled FitzHugh-Nagumo neuron models, effectively suppressing extreme events without altering the system's frequency.

Contribution

It introduces a straightforward mitigation strategy using constant bias in coupled neuron models, demonstrating its effectiveness across different coupling configurations.

Findings

Extreme events are suppressed in all coupled systems tested.

The mitigation does not affect the system's collective frequency.

Probability distribution confirms reduced extreme event occurrence.

Abstract

Formulating mitigation strategies is one of the main aspect in the dynamical study of extreme events. Apart from the effective control, easy implementation of the devised tool should also be given importance. In this work, we analyze the mitigation of extreme events in a coupled FitzHugh-Nagumo (FHN) neuron model utilizing an easily implementable constant bias analogous to a constant DC stimulant. We report the route through which the extreme events gets mitigated in $Two$, $Three$ and $N-$coupled FHN systems. In all the three cases, extreme events in the observable $\bar{x}$ gets suppressed. We confirm our results with the probability distribution function of peaks, $d_{max}$ plot and probability plots. Here $d_{max}$ is a measure of number of standard deviations that crosses the average amplitude corresponding to $\bar{x}_{max}$. Interestingly, we found that constant bias suppresses the extreme events without changing the collective frequency of the system.