Pattern formation through synchronization in systems of nonidentical autonomous oscillators

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2007

Author dc:creator

• Tönjes, Ralf

Contributors dc:contributor

• Blasius, Bernd

• Synchronisation
• Musterbildung
• Phasen-Gleichungen
• Phasen-Oszillatoren
• Kuramoto Modell
• synchronization
• pattern formation
• phase equations
• phase oscillators
• Kuramoto model

Statement dc:rights

• Creative Commons - Namensnennung, Nicht kommerziell, Keine Bearbeitung 2.0 Deutschland

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1467

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:1467