Replicate Periodic Windows in the Parameter Space of Driven Oscillators

TL;DR

This paper demonstrates that weak harmonic perturbations can replicate shrimp-shaped periodic windows in the parameter space of driven oscillators, aiding in chaos control by creating new regions of periodic behavior similar to existing orbits.

Contribution

It introduces a method to replicate periodic windows in driven oscillators' parameter space using weak harmonic perturbations, linking to chaos control.

Findings

Replicated periodic windows resemble original stable and unstable orbits.

Weak harmonic perturbation effectively creates new periodic regions.

Replicated windows facilitate chaos control in driven oscillators.

Abstract

In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have periodicity and pattern similar to stable and unstable periodic orbits already existent for the unperturbed oscillator. These features indicate that the reported replicate periodic windows are associated with chaos control of the considered oscillators.