Generally, synchronization in a network of chaotic systems depends on the underlying coupling topology. Recently, there have been several studies conducted to determine what features of this topology contribute to the ability to synchronize. A short diameter has been proposed by several authors as a means to facilitate synchronization whereas others point to features such as the homogeneity of the degree sequence. Recently, it has been shown that the degree sequence by itself is not sufficient to determine synchronizability. The purpose of this letter is to continue this study. For a given degree sequence, we construct two connected graphs with this degree sequence whose synchronizability can be quite different. In particular, we construct a graph with low synchronizability which improves upon previous bounds under certain conditions and we construct a graph which has synchronizability that is asymptotically maximal. On the other hand, we show analytically that for a random network model, homogeneity of the degree sequence is beneficial to synchronization.
By: Chai Wah Wu
Published in: RC23610 in 2005
LIMITED DISTRIBUTION NOTICE:
This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.
Questions about this service can be mailed to reports@us.ibm.com .