@phdthesis{Toenjes2007,
  author    = {T{\"o}njes, Ralf},
  title     = {Pattern formation through synchronization in systems of nonidentical autonomous oscillators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15973},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {This work is concerned with the spatio-temporal structures that emerge when non-identical, diffusively coupled oscillators synchronize. It contains analytical results and their confirmation through extensive computer simulations. We use the Kuramoto model which reduces general oscillatory systems to phase dynamics. The symmetry of the coupling plays an important role for the formation of patterns. We have studied the ordering influence of an asymmetry (non-isochronicity) in the phase coupling function on the phase profile in synchronization and the intricate interplay between this asymmetry and the frequency heterogeneity in the system. The thesis is divided into three main parts. Chapter 2 and 3 introduce the basic model of Kuramoto and conditions for stable synchronization. In Chapter 4 we characterize the phase profiles in synchronization for various special cases and in an exponential approximation of the phase coupling function, which allows for an analytical treatment. Finally, in the third part (Chapter 5) we study the influence of non-isochronicity on the synchronization frequency in continuous, reaction diffusion systems and discrete networks of oscillators.},
  language  = {en}
}