Delay-induced stochastic bursting in excitable noisy systems

TL;DR

This paper demonstrates how noise and delayed feedback induce coherent stochastic bursting in excitable theta-neurons, providing a point process model to analyze their statistical properties and deriving key parameters from Fokker-Planck equations.

Contribution

It introduces a novel point process model for stochastic bursting in excitable systems with delay, linking burst statistics to solutions of Fokker-Planck equations.

Findings

Noise and delay cause coherent bursting behavior.

The point process parameters can be derived from Fokker-Planck solutions.

The model accurately describes power spectrum and interspike intervals.

Abstract

We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated, is used to describe statistical properties such as the power spectrum and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate and the probability to induce a spike during the delay action, can be calculated from the solutions of a stationary and a forced Fokker-Planck equation.