Modulated escape from a metastable state driven by colored noise

TL;DR

This paper introduces a method to analyze excitable systems driven by colored noise by reducing them to white-noise systems with effective boundary conditions, enabling analytical insights into neuronal response properties.

Contribution

The authors develop a general reduction technique for colored noise in excitable systems, providing an analytical expression for neuronal response up to moderate frequencies.

Findings

Derived an analytical expression for neuronal linear response

Captured effects of colored noise via effective boundary conditions

Enabled characterization of oscillations in neuronal networks

Abstract

Many phenomena in nature are described by excitable systems driven by colored noise. The temporal correlations in the fluctuations hinder an analytical treatment. We here present a general method of reduction to a white-noise system, capturing the color of the noise by effective and time-dependent boundary conditions. We apply the formalism to a model of the excitability of neuronal membranes, the leaky integrate-and-fire neuron model, revealing an analytical expression for the linear response of the system valid up to moderate frequencies. The closed form analytical expression enables the characterization of the response properties of such excitable units and the assessment of oscillations emerging in networks thereof.