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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
112/2006

Global synchronization of discrete time dynamical network with a directed graph

Wenlian Lu and Tianping Chen

Abstract

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.

Received:
Oct 9, 2006
Published:
Oct 9, 2006
PACS:
05.45.Ra, 05.45.Xt, 02.10.Ox
Keywords:
synchronization, linearly coupled map lattices, diagonally stable, directed graph, spanning tree

Related publications

inJournal
2007 Repository Open Access
Wenlian Lu and Tianping Chen

Global synchronization of discrete time dynamical network with a directed graph

In: IEEE transactions on circuits and systems / 2, 54 (2007) 2, pp. 136-140