Pacemakers in a Cayley tree of Kuramoto oscillators

Abstract

In this work we study a system of Kuramoto oscillators with identical frequencies in a Cayley tree. Heterogeneity in the frequency distribution is introduced in the root of the tree, allowing for analytical calculations of the phases evolution. In this work we study a system of Kuramotooscillators with identical frequencies in a Cayley tree. Heterogeneity in the frequency distribution is introduced in the root of the tree, allowing for analytical calculations of the phases evolution. This simple case can be regarded as a starting point in order to understand how to extracttopological features of the connectivity pattern from the dynamic state of the system, and viceversa, for the general situation of a set of phase oscillators located on a tree-like network.