Controlling coherence of chaotic oscillators by means of two delayed feedbacks

TL;DR

This paper demonstrates that using two incommensurable delayed feedbacks on the Lorenz system significantly enhances control over chaotic oscillation coherence, outperforming single feedback methods without destroying chaos.

Contribution

It introduces a novel control method employing two delayed feedbacks to improve coherence control in chaotic systems, specifically applied to the Lorenz system.

Findings

Two incommensurable delays suppress phase diffusion by 2-3 orders of magnitude.

Single delay feedback suppresses phase diffusion by only 20 times.

The method maintains chaos while improving coherence control.

Abstract

We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest to feedback with multiple (incommensurable) delay times: (1) two delay times provide more flexibility in control than the single one; (2) some dynamic systems posses an inherent internal delay (e.g., traveling-wave tube), and the introducing of the second delayed feedback is a natural measure for dealing with stray effects brought about by the inherent one. Specifically, for the Lorenz system we show that two incommensurable delay times enable achieving suppression of the phase diffusion constant (quantifying the oscillation coherence) by 2-3 orders of magnitude without destruction of chaos, while the single one does by 20 times.