Principal Investigators: Barbara Gentz (Bielefeld), Yuri Kondratiev (Bielefeld)
Scientific Partners: Seung-Yeal Ha (SNU), Ki-Ahm Lee (SNU)
In this project, we will study various aspects of the dynamics of interacting systems in deterministic and random media.
Markov statistical dynamics
We will analyze the related kinetic equations. The main focus will be on dynamics given by fractional Fokker–Planck equations (FPEs).
For systems of coupled oscillators, we will study the effect of noise on synchronization and the subtle interplay between coupling strength, coupling structure and noise. A number of important questions regarding the onset of synchronization in the Kuramoto model will be investigated:
The following variants of the standard Kuramoto model and related models provide ample mathematical challenges and will be studied subsequently: