Controlling Nonlinear Stochastic Resonance by Harmonic Mixing

TL;DR

This paper explores how harmonic mixing signals can control nonlinear stochastic resonance in a double well potential, allowing for dynamic symmetry breaking, suppression, and enhanced response tuning in noisy systems.

Contribution

It introduces a method to control stochastic resonance using harmonic mixing, including phase and amplitude adjustments, and demonstrates the effectiveness of a two-state model approximation.

Findings

Harmonic mixing can dynamically break symmetry in stochastic resonance.

Adjusting phase difference suppresses the response regardless of noise level.

Resonances occur at higher harmonics of the noise strength and phase.

Abstract

We investigate the potential for controlling the effect of nonlinear Stochastic Resonance (SR) by use of harmonic mixing signals for an overdamped Brownian dynamics in a symmetric double well potential. The periodic forcing for harmonic mixing consists of a first signal with a basic frequency $\Omega$ and a second, superimposed signal oscillating at twice the basic frequency $2\Omega$. By variation of the phase difference between these two components and the amplitude ratios of the driving the phenomenon of SR becomes a priori controllable. The harmonic mixing dynamically breaks the symmetry so that the time- and ensemble-average assumes a non-vanishing value. Independently of the noise level, the response can be suppressed by adjusting the phase difference. Nonlinear SR then exhibits resonances at higher harmonics with respect to the applied noise strength and relative phase. The scheme of nonlinear SR via harmonic mixing can be used to steer the nonlinear response and to sensitively measure the internal noise strength. We further demonstrate that the full Fokker-Planck dynamics can be well approximated by a two-state model.