Complexity Aspects of the Classification of Synchronizing Graphs for Kuramoto Coupled Oscillators

Abstract

In this work, we give a complete presentation of the idea of synchronizing graphs for the Kuramoto model of coupled oscillators. We present the dynamical model and the main relationships between the system dynamics and the underlying interconnection topology. A synchronizing graph is an interconnection that ensures synchronization of all the oscillators for almost every initial condition. We present the main properties that help in the classification of synchronizing graphs and also some considerations about the structure of this family of graphs and the complexity of the classification task.