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

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

Global Synchronization Properties for Different Classes of Underlying Interconnection Graphs for Kuramoto Coupled Oscillators

This article deals with the general ideas of almost global syn-chronization of Kuramoto coupled oscillators and synchronizing graphs.We review the main existing results and introduce new results for someclasses of graphs that are important in network optimization: completek-partite graphs and what we have called Monma graph