Noise-controlled bistability in an excitable system with positive feedback

¹ Department of Physics, Humboldt-Universität zu Berlin - Newtonstr. 15, 12489 Berlin, Germany
² Laboratório de Neurodinâmica/Neurobiofísica, Universidade de São Paulo - São Carlos, SP, Brazil
³ Bernstein Center for Computational Neuroscience - Berlin, Germany

Received: 30 July 2014
Accepted: 3 October 2014

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 the asymptotic Fano factor of the event count (long-time variability) are 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.