Evaluation of Measures to Detect the Synchrony between Interacting Pendulum Oscillators

This paper evaluates five approaches for measuring the synchrony between four pendulum oscillators. It is well known that networked pendulum oscillators can be used to represent a simple model of brain electrical activity. A new synchrony measure, phase synchrony index (PSI), is proposed to detect synchrony. The Euclidean distance is used as a key measure of PSI between states of interacting pendulum oscillators. Four pendulum oscillators were coupled using a range of coupling values. Results indicate that existing methods can to some degree measure the synchronization. It was found that all of the methods evaluated, show an increase of synchrony when the coupling parameter is greater than 30. Moreover, our method and the multivariate synchronization measure approach, both detected synchrony for low coupling values where other methods failed.