Bachelor Project presentation - Timo Hilverts, University of Groningen

Title: The Kuramoto model on homogeneous ring networks for conformists and contrarians

Abstract:

Spontaneous synchronization is a fascinating concept. Yoshiki Kuramoto created a model to describe this synchronous behaviour for a population of coupled oscillators. He assumed such a coupling to be strictly positive, but for certain applications, it is also worth considering negative values. Oscillators with a positive coupling are called conformists and the ones with a negative coupling are called contrarians. We start by introducing the model when dealing with both conformists and contrarians. Thereafter, we use this model to analyse the behaviour of a homogeneous ring network for four and five oscillators, both analytically and numerically. For both four and five oscillators, we obtained a remarkable result. The equilibrium points which are stable when all coupling strengths are positive become unstable when introducing negative weights. The only case in which the stable equilibrium points can remain stable is whenever only one of the coupling strengths is negative. Eventually, we increase the number of oscillators, and conclude that the stronger the effect of the contrarians, the more difficult it is to achieve exact synchronization.

1st supervisor: dr. H. Jardon-Kojakhmetov

2nd assessor: dr. A.E. Sterk