Synchronization of Kuramoto oscillators in a bidirectional frequency-dependent tree network

TL;DR

This paper analyzes the conditions for frequency synchronization of Kuramoto oscillators in bidirectional tree networks with frequency-dependent coupling, providing bounds based on network structure and frequency distribution.

Contribution

It derives a sufficient condition for synchronization in frequency-dependent tree networks and applies it to an event-triggered synchronization algorithm in star networks.

Findings

Derived a bound on coupling strength for synchronization

Showed the bound depends on network structure and frequency distribution

Presented an event-triggered synchronization algorithm

Abstract

This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common coefficient and the exogenous frequency of its corresponding head oscillator. We derive a sufficient condition for the common coupling strength in order to guarantee frequency synchronization in tree networks. Moreover, we discuss the dependency of the obtained bound on both the graph structure and the way that exogenous frequencies are distributed. Further, we present an application of the obtained result by means of an event-triggered algorithm for achieving frequency synchronization in a star network assuming that the common coupling coefficient is given.