Speaker: Prof. Guanrong (Ron) Chen (Centre for Chaos and Complex Networks, City University of Hong Kong)
Title: A Graph-Theory Approach to Network Synchronizability Analysis
Abstract:
In this talk, we discuss how graph theory may be applied to the
analysis of complex network synchronization and synchronizability.
First, we observe that in the study of network synchronizability,
network structural parameters (for example, average path-length,
degree distribution, and betweenness centrality) have been the main
concern in the past. We show by simple examples of regular
symmetrical networks that these parameters may not be good to use -
two networks with exactly the same such structural parameters can
have very different synchronizabilities.
Then, we notice that another common perceptive is that a network
with more edges should be easier to sync. However, we give several
examples to show that generally adding new edges to a network can
either increase or decrease the network synchronizability.
Nevertheless, we will also show that for networks with disconnected
complementary graphs, adding edges never decreases their
synchronizabilities.
The most well-known result about the synchronizability of a general
complex network is that it relies on two major factors - the
Laplacian eigenvalues and the synchronized regions. In this regard,
we show that for any positive integer n, one can always find a
network with n disconnected synchronized regions, where bounded and
unbounded synchronized regions may coexist. Since a network with
unbounded synchronized regions is easier to apply and analyze, we
furthermore show how to design a simple rank-1 inner-linking matrix
to control the network synchronized regions to become unbounded.
This suggests an effective way for designing a simple feedback
controller to enhance the synchronizability of a given complex
network.
Bio:
Professor Chen received the MS degree in Computer Science from Sun
Yat-sen University, China in 1981 and the PhD degree in Applied
Mathematics from Texas A&M University, USA in 1987, with
Post-Doctorate research experience in nonlinear dynamics and
controls thereafter. He currently is a Chair Professor and the
founding director of the Centre for Chaos and Complex Networks at
the City University of Hong Kong, prior to which he was a tenured
Professor at the University of Houston, USA.
Professor Chen is an IEEE Fellow (since January 1997). He is
currently serving as the Editor-in-Chief of the IEEE Circuits and
Systems Magazine (since 2008), Deputy Editor-in-Chief of the
International Journal of Circuit Theory and Applications (since
2008) and the IEEE Transactions on Circuits and Systems, Part II
(2004-05) and Part I (2006-07), among others, and is Honorary
Professor at different ranks of twenty some universities worldwide.