Structural analysis of synchronization in networks of linear oscillators

TL;DR

This paper investigates how the structure of connections in networks of identical linear oscillators influences their ability to synchronize, providing conditions for achieving and guaranteeing synchronization across various coupling parameters.

Contribution

It introduces new conditions relating network structure to synchronization, including methods to ensure synchronization for all parameter values.

Findings

Synchronization depends on specific network interconnection conditions.

Conditions are provided for achieving synchronization with some coupling strengths.

Guarantees for synchronization across all admissible parameters are established.

Abstract

In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization and coupling structure is studied. Conditions on the interconnection under which synchronization can be achieved for some selection of coupling strengths are established. How to strengthen those conditions so that synchronization is guaranteed for all admissible parameter values is also presented.