Resonance between Noise and Delay

TL;DR

This paper introduces a simple stochastic binary model with delayed transitions, demonstrating through analysis and simulations that resonance phenomena occur between noise-induced oscillations and delay-induced oscillations.

Contribution

The work presents a novel delayed stochastic binary model and reveals resonance effects between noise and delay, supported by analytical and numerical evidence.

Findings

Resonance occurs between noise-driven and delay-driven oscillations.

The model exhibits oscillatory behavior influenced by both noise and delay.

Analytical and numerical methods confirm the resonance phenomena.

Abstract

We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise'' and ``delay''. We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.