Noise-controlled bistability in an excitable system with positive feedback

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.

arXiv comment6 pages, 4 figures, to be published in EPL

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Cited by in corpus (4)

• Noise-induced transitions in a double-well oscillator with nonlinear dissipation
• Two paradigmatic scenarios for inverse stochastic resonance
• Noise-induced transitions in a double-well excitable oscillator
• Delay-induced stochastic bursting in excitable noisy systems