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Forced Oscillations

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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing.

Jesús Casado-Pascual¹, David Cubero², Ferruccio Renzoni³

¹Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 4, 2014

Summary

This summary is machine-generated.

This study reveals universal features in nonlinear systems driven by two frequencies. The resonance width is smaller than predicted by Fourier analysis, with implications for sub-Fourier signal processing.

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Area of Science:

Nonlinear dynamics
Signal processing

Background:

Nonlinear systems exhibit complex behaviors when subjected to external forces.
Understanding the long-time response of such systems is crucial for various applications.

Purpose of the Study:

To derive an asymptotic expression for the time-averaged response of a nonlinear system driven by two frequencies.
To identify universal features of this asymptotic response, independent of specific model details.
To analyze the width of resonance phenomena in this context.

Main Methods:

A nonperturbative approach was employed to analyze the system's time-dependent behavior.
Asymptotic expressions were derived for the long-time limit of the system's response.
The resonance width was calculated by varying one driving frequency while keeping the other fixed.

Main Results:

Several universal features of the asymptotic response were identified, independent of model specifics.
An asymptotic expression for the resonance width was determined.
The calculated resonance width is smaller than the Fourier width by a factor dependent on the driving frequencies.

Conclusions:

The study provides insights into the long-time behavior of nonlinear systems under two-frequency forcing.
The findings have direct applications in sub-Fourier signal processing.
The identified universal features offer a generalized understanding of resonance in nonlinear systems.