Ghost-vibrational resonance

TL;DR

This paper explores how high-frequency forces induce resonance at missing fundamental frequencies in Duffing oscillators and demonstrates enhanced signal propagation in coupled oscillator networks without high-frequency forcing.

Contribution

It introduces the concept of high-frequency induced resonance at missing frequencies and analyzes its effects in single and coupled Duffing oscillators, extending ghost-stochastic resonance to a vibrational context.

Findings

High-frequency forces induce resonance at missing fundamental frequencies.

Analytical expression for response amplitude at the missing frequency.

Enhanced signal propagation in coupled oscillators without high-frequency forcing.

Abstract

Ghost-stochastic resonance is a noise-induced resonance at a fundamental frequency missing in the input signal. We investigate the effect of a high-frequency, instead of a noise, in a single Duffing oscillator driven by a multi-frequency signal $F(t)= \sum^n_{i=1} f_i \cos(\omega_i + \Delta \omega_0)t$, $\omega_i=(k+i-1)\omega_0$, where $k$ is an integer greater than or equal to two. We show the occurrence of a high-frequency induced resonance at the missing fundamental frequency $\omega_0$. For the case of the two-frequency input signal, we obtain an analytical expression for the amplitude of the periodic component with the missing frequency. We present the influence of the number of forces $n$, the parameter $k$, the frequency $\omega_0$ and the frequency shift $\Delta \omega_0$ on the response amplitude at the frequency $\omega_0$. We also investigate the signal propagation in a network of unidirectionally coupled Duffing oscillators. Finally, we show the enhanced signal propagation in the coupled oscillators in absence of a high-frequency periodic force.