B. Dynamics of interacting systems

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).

Coupled oscillators
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:

  • Does noise facilitate synchronization?
  • Through which metastable states does the system pass to achieve synchronization?
  • How do the answers depend on the coupling structure?

The following variants of the standard Kuramoto model and related models provide ample mathematical challenges and will be studied subsequently:

  • A stochastic Kuramoto model with inertia and interaction frustration.
  • Different types of random couplings.
  • Flocking dynamics for the noisy Cucker–Smale model.

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