Global and local synchronization of general multi-linked delayed complex dynamical networks

Abstract

This paper investigates the phenomena of a new and general multi-linked complex network with delayed nodes and couplings. Via constructing Lyapunov-Krasovskii function and using inequality technique, the criteria for locally exponential synchronization and globally asymptotical synchronization are derived. The latter neither requires the outer-coupling configuration matrix to be symmetric and irreducible nor needs the network to be linearized at its synchronization state, it is obtained by Kronecker product method. Finally, a numerical example illustrates the theoretical results. © 2009 Springer Berlin Heidelberg.