23.05.2018 14:30 Prof. Dr. Barbara Gentz (Universität Bielefeld):
Synchronization in the noisy Kuramoto model of oscillatorsMI HS 3 (Boltzmannstr. 3, 85748 Garching)

Synchronization is a collective phenomenon observed, for instance, in fireflies, in a clapping audience or in the pacemaker cells in the cardiac pacemaker. Mathematical models for this type of synchronization are based on systems of coupled oscillators. We will start by reviewing the Kuramoto model, introduced by Yoshiki Kuramoto in 1975. It has been successfully analyzed, including many generalizations. In particular, the emergence of synchronization in the Kuramoto model is well understood by now, while much less is known about the effect of noise on sychronization of Kuramoto oscillators. We will address the questions of emergence and of persistence of synchronziation in the presence of random perturbations for an arbitrary \(finite\) number of non-identical oscillators. The main results and ideas will be explained in the special case of two oscillators which is particularly easy to study since the model can be reduced to a stochastic version of the Adler equation in this case.