Control of Hierarchical Networks by Coupling to an External Chaotic System

TL;DR

This paper demonstrates that coupling hierarchical networks of chaotic oscillators to an external dissimilar chaotic system effectively suppresses chaos and achieves control, regardless of the coupling pathway or hierarchy level.

Contribution

It introduces a novel control method using an external chaotic system to suppress chaos in hierarchical networks of oscillators, regardless of coupling pathway.

Findings

Chaos suppression at high coupling strength

Synchronization at specific hierarchy levels

High basin stability for fixed points

Abstract

We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the mean-field of the oscillators below it in the hierarchy, and couples diffusively to the oscillator above it in the hierarchy. We find that coupling to one dissimilar external system manages to suppress the chaotic dynamics of all the oscillators in the network at sufficiently high coupling strength. This holds true irrespective of whether the connection to the external system is direct or indirect through oscillators at another level in the hierarchy. Investigating the synchronization properties show that the oscillators have the same steady state at a particular level of hierarchy, whereas the steady state varies across different hierarchical levels. 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. These quantitative results indicate the easy controllability of hierarchical networks of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.