Robustness of Optimal Synchronization in Real Networks

TL;DR

This paper experimentally investigates how connection topology affects synchronization in fiber-optic networks of chaotic oscillators, revealing non-monotonic synchronization landscapes and the impact of eigenvector degeneracy under real-world conditions.

Contribution

It demonstrates the influence of eigenvector degeneracy on synchronization behavior in real networks, highlighting effects overlooked by traditional eigenvalue analysis.

Findings

Synchronization landscape is non-monotonic and cusp-like.

Networks with identical eigenvalues can behave differently.

Eigenvector degeneracy affects synchronization in noisy, mismatched conditions.

Abstract

Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted non-monotonic, cusp-like synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.