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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 

 

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