Theory for Inverse Stochastic Resonance in Nature

TL;DR

This paper presents a theoretical framework explaining inverse stochastic resonance (ISR) as a phenomenon arising from asymmetric bistable potential functions, with implications for understanding natural systems exhibiting noise-induced response depression.

Contribution

It develops a theoretical model linking ISR to potential function asymmetry and metastability, providing conditions for its emergence in natural bistable systems.

Findings

ISR occurs with asymmetric potential functions and metastable high activity states.

The potential shape explains the emergence of non-standard stochastic resonance.

The framework predicts ISR in various natural systems sharing these features.

Abstract

The inverse stochastic resonance (ISR) phenomenon consists in an unexpected depression in the response of a system under external noise, e.g., as observed in the behavior of the mean-firing rate in some pacemaker neurons in the presence of moderate values of noise. A possible requirement for such behavior is the existence of a bistable regime in the behavior of these neurons. We here explore theoretically the possible emergence of this behavior in a general bistable system, and conclude on conditions the potential function which drives the dynamics must accomplish. We show that such an intriguing, and apparently widely observed, phenomenon ensues in the case of an asymmetric potential function when the high activity minimum state of the system is metastable with the largest basin of attraction and the low activity state is the global minimum with a smaller basin of attraction. We discuss on the relevance of such a picture to understand the ISR features and to predict its general appearance in other natural systems that share the requirements described here. Finally, we report another intriguing non-standard stochastic resonance in our system, which occurs in the absence of any weak signal input into the system and whose emergence can be explained, with the ISR, within our theoretical framework in this paper in terms of the shape of the potential function.