Controlling synchronous patterns in complex networks

TL;DR

This paper introduces a novel control framework for stabilizing specific synchronous patterns in complex networks of chaotic oscillators by leveraging permutation symmetries and pinning control, validated through simulations and experiments.

Contribution

The authors develop a new method to control synchronization patterns in complex networks using a small control network and pinning coupling, applicable to any network symmetry.

Findings

Existence of a critical pinning strength for stabilization

Control method effective on artificial and real networks

Experimental validation with coupled chaotic circuits

Abstract

Although the set of permutation symmetries of a complex network can be very large, few of the symmetries give rise to stable synchronous patterns. Here we present a new framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators. Specifically, according to the network permutation symmetry, we design a small-size and weighted network, namely the control network, and use it to control the large-size complex network by means of pinning coupling. We argue mathematically that for \emph{any} of the network symmetries, there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized. The feasibility of the control method is verified by numerical simulations of both artificial and real-work networks, and is demonstrated by experiment of coupled chaotic circuits. Our studies pave a way to the control of dynamical patterns in complex networks.