Complex Network Geometry and Frustrated Synchronization

TL;DR

This paper explores how the geometry and spectral properties of complex networks influence the synchronization behavior of coupled oscillators, revealing that network structure can induce frustrated synchronization.

Contribution

It introduces a novel model linking network geometry, spectral dimension, and synchronization, providing new insights into the interplay between structure and dynamics.

Findings

Networks exhibit frustrated synchronization over various coupling strengths.

Synchronization properties are directly influenced by the spectral dimension.

The model combines small world features with tunable spectral properties.

Abstract

The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled oscillators in the context of a simplicial complex model of manifolds called Complex Network Manifold. The networks generated by this model combine small world properties (infinite Hausdorff dimension) and a high modular structure with finite and tunable spectral dimension. We show that the networks display frustrated synchronization for a wide range of the coupling strength of the oscillators, and that the synchronization properties are directly affected by the spectral dimension of the network.