Divergent Signal-to-Noise Ratio and Stochastic Resonance in Monostable Systems

TL;DR

This paper introduces a class of monostable systems where the signal-to-noise ratio increases with noise, diverging at infinite noise, revealing a new form of stochastic resonance with broad scientific implications.

Contribution

It demonstrates a novel phenomenon where SNR diverges with noise in monostable systems, supported by a scaling law and specific examples.

Findings

SNR always increases with noise in the studied systems

Divergence of SNR at infinite noise levels

Stochastic resonance occurs in certain monostable systems

Abstract

We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the signal-to-noise ratio and implies the appearance of stochastic resonance in some monostable systems. We outline applications of our results to a wide variety of systems pertaining to different scientific areas. Two particular examples are discussed in detail.