# Topological Control of Synchronization Patterns: Trading Symmetry for Stability

## TL;DR

This paper reveals that breaking symmetry in network structures can enhance synchronization stability, challenging traditional views, and provides algorithms for topological control of synchronization patterns.

## Contribution

It demonstrates that symmetry breaking can improve synchronization stability in networks, supported by experimental validation and optimization algorithms.

## Key findings

- Symmetry breaking enhances cluster synchronizability.
- Experimental validation confirms robustness against noise.
- Optimization algorithms improve network structure for desired synchronization.

## Abstract

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is believed to enhance the stability of identical synchronization. Yet, here we show that the synchronizability of almost any symmetry cluster in a network of identical nodes can be enhanced precisely by breaking its structural symmetry. This counterintuitive effect holds for generic node dynamics and arbitrary network structure and is, moreover, robust against noise and imperfections typical of real systems, which we demonstrate by implementing a state-of-the-art optoelectronic experiment. These results lead to new possibilities for the topological control of synchronization patterns, which we substantiate by presenting an algorithm that optimizes the structure of individual clusters under various constraints.