Controlling symmetries and clustered dynamics of complex networks

TL;DR

This paper presents a method to control symmetries and induce specific clustered synchronization patterns in complex networks by minimally perturbing their connectivity, with applications in robotics, power grids, and autonomous systems.

Contribution

It introduces a novel approach to manipulate network symmetries and stabilize desired clustered states through optimized minimal topological modifications.

Findings

The method effectively enforces targeted synchronization patterns.

Stability conditions for the patterns are derived.

The approach is validated with practical examples.

Abstract

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivity, either by adding new edges or by adding/removing links together with modifying their weights. By solving suitable optimization problems, we furthermore guarantee that changes made on the existing topology are minimal. The conditions for the stability of the enforced pattern are derived for the general case, and the performance of the method is illustrated with paradigmatic examples. Our results are relevant to all the practical situations in which coordination of the networked systems into diverse groups may be desirable, such as for teams of robots, unmanned autonomous vehicles, power grids and central pattern generators.