Synchronization versus neighborhood similarity in complex networks of non-identical oscillators

TL;DR

This paper investigates how different assignment patterns of non-identical oscillators in complex networks affect synchronization, revealing that homogeneous networks synchronize more easily but initial partial synchronization occurs faster in similar patterns.

Contribution

It introduces the Total Dissonance measure to quantify neighbor dissimilarity and compares the effects of Similar, Dissimilar, and Neutral patterns on synchronization behavior.

Findings

Homogeneous networks require higher coupling for phase-locking.

Similar patterns lead to faster initial partial synchronization.

Neutral patterns exhibit intermediate synchronization characteristics.

Abstract

Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical interacting oscillators. Three connection configurations found in Nature are considered here: Similar, Dissimilar and Neutral patterns. These strategies correspond respectively to oscillators alike, distinct and indifferent relate to its neighbors. To construct such scenarios we define a vertex weighted graph measure, the Total Dissonance, which comprises the sum of the dissonances between all neighbor oscillators in the network. Our numerical simulations show that the more homogeneous is a network, the higher tend to be both the coupling strength required to phase-locking and the associated final phase configuration spread over the circle. On the other hand, the initial spread of partial synchronization occurs faster for Similar patterns in comparison to Dissimilar ones, while neutral patterns are an intermediate situation between both extremes.