Noise-controlled bistability in an excitable system with positive feedback

TL;DR

This paper investigates how noise influences bistability in an excitable system with positive feedback, revealing controllable state probabilities and significant effects on event regularity and variability.

Contribution

It demonstrates noise-controlled bistability and its impact on event regularity in excitable systems with positive feedback, a novel insight into noise-induced dynamics.

Findings

Noise intensity controls the occupation probabilities of low and high activity states.

Bistability leads to giant variability in event timing when states are equally likely.

Long-range correlations amplify long-time variability in event generation.

Abstract

We study the interplay between noise and a positive feedback mechanism in an excitable system that generates events. We show that such a system can exhibit a bistability in the dynamics of the event generation (states of low and high activity). The stability of the two states is determined by the strength of the noise such that a change of noise intensity permits complete control over the probabilities with which the two states are occupied. The bistability also has strong implications for the regularity of the event generation. While the irregularity of the interevent interval (short-time variability) and of the asymptotic Fano factor of the event count (long-time variability) is limited if the system is only in one of the two states, we show that both measures of variability display giant values if both states are equally likely. The long-time variability is additionally amplified by long-range positive correlations of the interevent intervals.