Coherent response of a stochastic nonlinear oscillator to a driving force: analytical characterization of the spectral signatures

TL;DR

This paper analytically investigates how a noisy nonlinear oscillator driven by a sinusoidal force produces supernarrow spectral peaks, revealing the underlying mechanisms and parameter conditions that lead to this coherent response.

Contribution

It provides an analytical framework using averaging techniques to explain the spectral signatures in a driven stochastic nonlinear oscillator, connecting linearized dynamics to observed peaks.

Findings

Spectral peaks are linked to characteristics of linearized stochastic equations.

Peak widths decrease when characteristic frequencies near attractors align with the driving frequency.

Parameter variations can significantly enhance the coherence of the oscillator's response.

Abstract

We study the dynamics of a classical nonlinear oscillator subject to noise and driven by a sinusoidal force. In particular, we give an analytical identification of the mechanisms responsible for the supernarrow peaks observed recently in the spectrum of a mechanical realization of the system. Our approach, based on the application of averaging techniques, simulates standard detection schemes used in practice. The spectral peaks, detected in a range of parameters corresponding to the existence of two attractors in the deterministic system, are traced to characteristics already present in the linearized stochastic equations. It is found that, for specific variations of the parameters, the characteristic frequencies near the attractors converge on the driving frequency, and, as a consequence, the widths of the peaks in the spectrum are significantly reduced. The implications of the study to the control of the observed coherent response of the system are discussed.