Controlling Mackey--Glass chaos

TL;DR

This paper introduces a novel control method for the Mackey-Glass system that transforms its chaotic behavior into predictable dynamics by using domain decomposition and state-dependent delays.

Contribution

It presents a new approach to chaos control in delay systems by forcing solutions into monotone feedback domains and employing state-dependent delays for stabilization.

Findings

The method guarantees the elimination of chaos in the Mackey-Glass system.

Domain decomposition is effective with common control terms.

State-dependent delays provide an alternative chaos control scheme.

Abstract

The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for chaos control: we prove that with well chosen control parameters, all solutions of the system can be forced into a domain where the feedback is monotone, and by the powerful theory of delay differential equations with monotone feedback we can guarantee that the system is not chaotic any more. We show that this domain decomposition method is applicable with the most common control terms. Furthermore, we propose an other chaos control scheme based on state dependent delays.