Graph Topologies and the Synchronization of Coupled Dynamical Systems

Graph Topologies and the Synchronization of 

Coupled Dynamical Systems
 

 Fatihcan M. Atay, Max Planck Institute for Mathematics in the Sciences
 

The study of synchronization is a very active field of research in the physical, 

biological, and engineering sciences. Recent discoveries related to the synchronization of 

chaotic systems or systems with time delays continue to add to the excitement in this area. 

This talk will focus on the role of the connection topology in synchronization, which can 

be mathematically characterized through the spectrum of a Laplacian operator defined 

on the underlying graph. Large networks are typically described by their degree distribution, 

that is, the fraction of nodes having a certain number of connections. I will present a proof 

that shows that the degree distribution of a graph does not suffice to determine its 

synchronizability. More precisely, a fairly large class of degree distributions have 

realizations which are arbitrarily poor synchronizers. This class includes many common 

architectures, such as regular graphs, the random graphs of Erdös and Renyi, and the 

recently popular small-world and scale-free graphs. The proof is constructive in nature, 

and also serves as an algorithm for the construction of non-synchronizing networks.
 

December 21, 2004 at 15:00, FENS G035