Time Frequency Analysis of the Kuramoto Model

01 Jun 2016

Abstract: The phenomenon of synchronisation is studied by means of the Kuramoto model. This model describes a large population of coupled oscillators with natural frequencies taken from a narrow distribution. It is assumed that the coupling between the oscillators is mean-field and purely sinusoidal. We follow Kuramoto’s analysis to obtain a formula for the critical coupling. Then the properties of the Kuramoto model are studied with the aid of Poincaré maps. We then conclude with a time-frequency analysis of the order parameter. With the aid of this time-frequency analysis we were able to detect partial synchronisation.

Supervisor: Holger Waalkens (University of Groningen)

Have a look at my thesis here (pdf)

Code from Appendix B.1 (Computes the trajectory of the order parameter of the Kuramoto model.)

Code from Appendix B.2 (Calculates the wavelet transform of a single trajectory of the 3D system.)

Code from Appendix B.3 (Converts the data to images.)