第54回「非線形・統計力学とその周辺」セミナーのご案内

日時：2004年3月16日（火）15:00から

場所：京都大学工学部総合校舎２１３室

講演者：Prof. Ying-Cheng Lai（Arizona State Univ.）

講演題目： Synchronization in complex networks

講演要旨：

In their seminal work, Watts and Strogatz showed that the addition
of a small number of shortcut links to an otherwise regular, locally
connected network can greatly reduce the average network distance
between two nodes while keeping the network locally clustered.
Such networks are said to have the small-world (SW) property. A
wealth of examples from real-world networks including both artificial
and natural systems, have been identified to have the SW property.
Another seemingly generic feature of networks in the real-world is
the scale-free (SF) nature of the connectivity distribution signified
by its power-law form. Barabasi and Albert suggested a model of
growing networks, in which preferential attachment of new links
to nodes with higher connectivity results in the SF property.
SF networks have particularly small average network distance due
to the heterogeneity in the connectivity distribution.

So far, much research has been focused on the structural properties of
SW and SF network models. Despite the widespread belief that these
structural properties must have significant impact on dynamical
processes taking place on such networks, there has been little work
addressing this issue. Most of such work dealt with synchronization
of oscillators whose topology of interaction has either the SW or the
SF property, showing that it leads to improved synchronizability when
compared to local lattice topology.  A general argument underlying
this phenomenon is that communications between oscillators are more
efficient because of the smaller average network distance.  But, does
smaller average network distance improve synchronizability?

Surprisingly, we recently discovered that networks with a homogeneous
distribution of connectivity are more synchronizable than heterogeneous
ones (e.g., scale-free networks), even though the average network
distance is larger. Some degree of homogeneity is then expected in
naturally evolved structures, such as neural networks, where
synchronizability is desirable.

The talk aims to explain the finding by focusing on the stability of
the synchronous dynamics in terms of the topology of the underlying
complex network. Numerical support will be presented and implications
of the result will be discussed.