A Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators

Abstract

Sufficient conditions for almost global synchronization in acyclic networks of Kuramoto oscillators with heterogeneous coupling strengths and natural frequencies are presented. The result is established by employing the recently developed Leonov function framework for systems whose dynamics are periodic for all state variables. The synchronization property is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria. The implications of these conditions on the network topology, the oscillator's coupling strengths and natural frequencies are discussed. Finally, the results are illustrated via a numerical example.