Reduction of colored noise in excitable systems to white noise and dynamic boundary conditions

TL;DR

This paper introduces a new method to analyze how colored noise affects excitable systems like neurons, simplifying existing models and enabling future extensions beyond first-order approximations.

Contribution

It presents an alternative derivation of the transfer function for neuron models under colored noise, explicitly incorporating time-dependent boundary conditions for improved accuracy.

Findings

Derivation of transfer function with explicit boundary conditions

Simplification of the white noise analogy for neuron models

Framework for extending beyond first-order perturbation theory

Abstract

A recent study on the effect of colored driving noise on the escape from a metastable state derives an analytic expression of the transfer function of the leaky integrate-and-fire neuron model subject to colored noise. Here we present an alternative derivation of the results, taking into account time-dependent boundary conditions explicitly. This systematic approach may facilitate future extensions beyond first order perturbation theory. The analogy of the quantum harmonic oscillator to the LIF neuron model subject to white noise enables a derivation of the well known transfer function simpler than the original approach. We offer a pedagogical presentation including all intermediate steps of the calculations.