Synchronization has been the topic of my Ph.D. thesis, and since then I have studied systematically various aspects of this interesting collective effect, such as synchronization of

  • nonidentical oscillators in lattices, 

  • identical oscillators in disordered media (random networks),

  • oscillators subject to colored noise and

  • synchronization of stochastic discrete state oscillators.

I have been studying the possibility of an analytical description of phase synchronization for chaotic oscillators for some years now.


Random processes

The topic of my Diploma thesis was Spectral Properties of a Stochastic Predator-Prey System. Over the years  Langevin equations, the Master equation and the Fokker-Planck equation have become familiar tools. The subjects of my research have been

  • the analytical description of Zipf's law as a natural consequence of self-similar branching with application to the analysis of the distribution of chess openings,

  • stability of the incoherent state in the Kuramoto Model with randomly fluctuating frequencies, and

  • synchronization of forced or coupled Markov-chain cycles.

I am currently researching spectral properties of the fractional Fokker-Planck equation for Levy flights in potentials.