Bursting oscillations induced by small noise

TL;DR

This paper investigates how small stochastic noise induces irregular bursting in a neuron model, identifying two distinct statistical regimes based on whether fast or slow subsystem fluctuations dominate.

Contribution

It introduces two classes of noise-perturbed slow-fast systems for bursting and derives Poincare maps to analyze burst statistics and spike distributions.

Findings

Type I bursting is driven mainly by fast subsystem fluctuations.

Type II bursting is dominated by slow subsystem perturbations.

The analysis explains the distribution of spikes per burst and their dependence on parameters.

Abstract

We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting patterns are studied in the present work. In particular, we identify two principal statistical regimes associated with the noise-induced bursting. In the first case, (type I) bursting oscillations are created mainly due to the fluctuations in the fast subsystem. In the alternative scenario, type II bursting, the random perturbations in the slow dynamics play a dominant role. We propose two classes of randomly perturbed slow-fast systems that realize type I and type II scenarios. For these models, we derive the Poincare maps. The analysis of the linearized Poincare maps of the randomly perturbed systems explains the distributions of the number of spikes within one burst and reveals their dependence on the small and control parameters present in the models. The mathematical analysis of the model problems is complemented by the numerical experiments with a generic Hodgkin-Huxley type model of a bursting neuron.