# Stochastic bursting in unidirectionally delay-coupled noisy excitable systems

## TL;DR

This paper demonstrates that stochastic bursting occurs in delay-coupled noisy excitable systems due to the interplay of time delays and noise, with analytical descriptions matching simulations.

## Contribution

It introduces an analytical framework for understanding stochastic bursting in delay-coupled excitable systems, highlighting the role of timescale separation and leader-follower dynamics.

## Key findings

- Stochastic bursting observed in delay-coupled noisy systems.
- Analytical spike statistics and correlations derived.
- Good agreement between theory and simulations.

## Abstract

We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by idealized coupled point processes with a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in a good agreement with the simulations with a network of theta-neurons.