Remote synchronization reveals network symmetries and functional modules

TL;DR

This paper investigates how network symmetries influence remote synchronization in a Kuramoto model with phase frustration, revealing that symmetric nodes can synchronize despite being distant, with implications for understanding brain network functionality.

Contribution

It introduces a novel analysis of remote synchronization driven by network symmetries in a frustrated Kuramoto model, linking structural symmetry to functional modules.

Findings

Symmetric nodes can fully synchronize despite being distant.

Frustration parameter influences phase distribution.

Brain network analysis suggests anatomical symmetry affects neural synchronization.

Abstract

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.