Pattern recognition tools for output-based classification of synchronised Kuramoto states

Abstract

Kuramoto oscillators are known to exhibit multiple synchrony where the states of individual oscillators synchronise in groups. We present a method for output-based classification of synchronised states in networks of Kuramoto oscillators using an artificial neural network for pattern recognition. Outputs of synchronised states are represented by spectrograms, in other words “fingerprint”, on which an artificial neural network of stacked autoencoders is then trained to classify these fingerprints and thus the different types of synchrony. We illustrate the approach for a Kuramoto model with N = 4 oscillators which exhibits synchrony of five types. We provide performance metrics for learning and training data which demonstrat that the approach reaches high levels of reliability.