Controlling coherence of chaotic oscillators by means of two delayed feedbacks

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.