Stochastic Resonance in Time-delayed Bistable Systems Driven by Weak Periodic Signal

TL;DR

This paper investigates how time-delayed feedback influences stochastic resonance in bistable systems driven by weak periodic signals, revealing that feedback can either suppress or enhance resonance depending on its sign and strength.

Contribution

It provides a theoretical analysis of the effects of time delay and feedback strength on stochastic resonance, including derivation of effective potential and SNR modulation.

Findings

Time delay modulates the shape of potential wells.

Feedback strength affects the maximum SNR.

Negative feedback suppresses, positive feedback promotes stochastic resonance.

Abstract

We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of signal. The maximum of SNR decreases with increasing the feedback intensity $\epsilon$. When $\epsilon$ is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.