Exact results for power spectrum and susceptibility of a leaky integrate-and-fire neuron with two-state noise

TL;DR

This paper derives exact formulas for the power spectrum and susceptibility of a leaky integrate-and-fire neuron influenced by dichotomous noise, revealing unique periodic features and validating results with simulations.

Contribution

It provides the first exact analytical expressions for these properties in a neuron model driven by asymmetric dichotomous noise, highlighting limitations of this noise approximation.

Findings

Exact expressions for power spectrum and susceptibility derived

Results agree well with numerical simulations

Periodic structures in the response functions identified and discussed

Abstract

The response properties of excitable systems driven by colored noise are of great interest, but are usually mathematically only accessible via approximations. For this reason, dichotomous noise, a rare example of a colored noise leading often to analytically tractable problems, has been extensively used in the study of stochastic systems. Here, we calculate exact expressions for the power spectrum and the susceptibility of a leaky integrate-and-fire neuron driven by asymmetric dichotomous noise. While our results are in excellent agreement with simulations, they also highlight a limitation of using dichotomous noise as a simple model for more complex fluctuations: Both power spectrum and susceptibility exhibit an undamped periodic structure, the origin of which we discuss in detail.