Suppression of chaos through coupling to an external chaotic system

TL;DR

This paper demonstrates that coupling chaotic oscillators to an external chaotic system, even if dissimilar, can effectively suppress their intrinsic chaos and stabilize them to fixed points, offering a new control strategy.

Contribution

It reveals that dissimilar external chaotic systems can suppress chaos in oscillators, expanding the understanding of chaos control methods beyond synchronization.

Findings

Dissimilar external chaos can stabilize oscillators to fixed points.

High coupling strength enhances control effectiveness.

Coupling to hyper-chaotic systems also suppresses chaos.

Abstract

We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system manages to suppress the intrinsic chaos of the oscillators to fixed point dynamics, at sufficiently high coupling strengths. So, while synchronization is induced readily by coupling to an identical external system, control to fixed states is achieved only if the external system is dissimilar. We quantify the efficacy of control by estimating the fraction of random initial states that go to fixed points, a measure analogous to basin stability. Lastly, we indicate the generality of this phenomenon by demonstrating suppression of chaotic oscillations by coupling to a common hyper-chaotic system. These results then indicate the easy controllability of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.