An exactly solvable nonlinear model: Constructive effects of correlations between Gaussian noises

TL;DR

This paper analyzes a two-noise Gaussian system revealing how correlations can induce stochastic resonance, localization, and distribution tails, and proposes a method to enhance signal transmission by parameter tuning.

Contribution

It introduces an exactly solvable nonlinear model demonstrating the constructive effects of correlated Gaussian noises on system behavior.

Findings

Correlations induce stochastic resonance and localization.

Variance exhibits nonmonotonic dependence on noise intensity.

Parameter tuning can improve external signal transmission.

Abstract

A system with two correlated Gaussian white noises is analysed. This system can describe both stochastic localization and long tails in the stationary distribution. Correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance. A method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed.