Predicting the coherence resonance curve using a semi-analytical treatment

TL;DR

This paper develops a semi-analytical approach to predict the coherence resonance curve in nonlinear excitable systems, providing a simple formula for the normalized variance of inter-spike intervals that matches numerical results.

Contribution

It introduces a novel semi-analytical method to accurately predict coherence resonance behavior in excitable systems, validated on two models.

Findings

The formula accurately predicts the unimodal profile of $V_N$.

Good agreement between semi-analytical predictions and numerical simulations.

Applicable to different excitable system models.

Abstract

Emergence of noise induced regularity or Coherence Resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance ($V_{N}$) of inter spike time intervals, which is a measure of regularity in such systems, has a unimodal profile. Our semi-analytic treatment of the associated spiking process produces a general yet simple formula for $V_{N}$, which we show is in very good agreement with numerics in two test cases, namely the FitzHugh-Nagumo model and the Chemical Oscillator model.