Phase tracking by weight adaptation for coupled Kuramoto oscillators #

Faizah Alanazi

Poster session

Abstract #

We consider synchronization between a pair of Kuramoto oscillators. One oscillator plays the role of a training oscillator, the other a learning oscillator. Our main result is an adaptive strategy which tunes the Kuramoto coupling strengths (weights) and the Kuramoto frequencies in the learning oscillator to achieve tracking between the phases of the training and learning oscillators. Tracking is proved using a Lyapunov stability approach. The adaptive strategy also guarantees partial convergence of the learning weights and frequencies to those of the training oscillator. Partial convergence is characterised by linear dependence of the phase differences of the states of the training oscillator. The results are illustrated by a 4-node oscillator with a variety of clustering configurations (2+2, 3+1, etc).