Locals vs. global synchronization in networks of non-identical Kuramoto oscillators
Centre for Complex Systems Science, CSIRO Marine and Athmospheric Research, GPO Box 284, Crace Canberra, ACT, 2601, Australia
Corresponding author: a Markus.Brede@Csiro.au
Revised: 11 February 2008
Published online: 21 March 2008
In this paper networks that optimize a combined measure of local and global synchronizability are evolved. It is shown that for low coupling improvements in the local synchronizability dominate network evolution. This leads to an expressed grouping of elements with similar native frequency into cliques, allowing for an early onset of synchronization, but rendering full synchronization hard to achieve. In contrast, for large coupling the network evolution is governed by improvements towards full synchronization, preventing any expressed community structure. Such networks exhibit strong coupling between dissimilar oscillators. Albeit a rapid transition to full synchronization is achieved, the onset of synchronization is delayed in comparison to the first type of networks. The paper illustrates that an early onset of synchronization (which relates to clustering) and global synchronization are conflicting demands on network topology.
PACS: 89.75.-k – Complex systems / 05.45.Xt – Synchronization; coupled oscillators / 89.75.Fb – Structures and organization of complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008