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Global synchronization of discrete time dynamical network with a directed graph
Wenlian Lu and Tianping Chen
We investigate synchronization of linearly coupled map lattices with asymmetric and irreducible coupling matrices. In terms of graph theory, the coupling matrix represents a directed graph. In case that the uncoupled map satisfies Lipschitz conditions, a criterion of global synchronization of the coupled system is derived. With this criterion, we investigate how synchronizability depends on the coupling matrix as well as graph topology. In Wu 2005, the author proved that for linearly coupled continuous networks, chaos can be synchronized if and only if the graph contains a spanning tree. In this paper, we show that this conclusion also holds for linearly coupled map lattices.