講演者：Prof. Ying-Cheng Lai（Arizona State Univ.）
講演題目： Synchronization in complex networks
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.