Synchrony-optimized Networks of Non-identical Kuramoto Oscillators

TL;DR

This paper presents a method to design coupling networks for non-identical Kuramoto oscillators that optimize synchrony, revealing how heterogeneity influences network structure and proposing rules to enhance synchronizability.

Contribution

It introduces a novel approach to generate synchrony-optimized networks for heterogeneous oscillators, extending stability analysis beyond identical cases.

Findings

Heterogeneity in oscillators leads to heterogeneity in optimal networks.

Anti-correlation of native frequencies among neighbors enhances synchrony.

Frequency magnitude correlates positively with node degree for better synchronization.

Abstract

In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling network to its synchronizability. These relations were previously only established from a linear stability analysis of the identical oscillator case. We further demonstrate that the heterogeneity in the oscillator population produces heterogeneity in the optimal coupling network as well. Two rules for enhancing the synchronizability of a given network by a suitable placement of oscillators are given: (i) native frequencies of adjacent oscillators must be anti-correlated and (ii) frequency magnitudes should positively correlate with the degree of the node they are placed at.