Switching chaos on/off in Duffing oscillator

TL;DR

This paper presents a simple, cost-effective method to control chaos in the Duffing oscillator by adjusting the shape of the forcing function, demonstrated through analytical, numerical, and experimental results.

Contribution

It introduces a novel, straightforward approach to switch chaos on or off in nonlinear oscillators by modifying forcing shape, with broad educational potential.

Findings

Effective chaos suppression demonstrated

Chaos generation achieved through forcing shape adjustment

Method validated analytically, numerically, and experimentally

Abstract

Periodic forcing of nonlinear oscillators generates a rich and complex variety of behaviors, ranging from regular to chaotic behavior. In this work we seek to control, i.e., either suppress or generate, the chaotic behavior of a classical reference example in books or introductory articles, the Duffing oscillator. For this purpose, we propose an elegant strategy consisting of simply adjusting the shape of the time-dependent forcing. The efficiency of the proposed strategy is shown analytically, numerically and experimentally. In addition due to its simplicity and low cost such a work could easily be turned into an excellent teaching tool.