Pinning synchronization of a general complex dynamical network

Authors:
Wenlin Li;Zhenhong Liu;Jing Miao
Affiliations:
College of Mathematics and Information Science, He'nan Normal University, Xinxiang, China;College of Mathematics and Information Science, He'nan Normal University, Xinxiang, China;College of Mathematics and Information Science, He'nan Normal University, Xinxiang, China
Venue:
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Year:
2009

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The Structure and Dynamics of Networks: (Princeton Studies in Complexity)

The Structure and Dynamics of Networks: (Princeton Studies in Complexity)
Brief paper: Pinning adaptive synchronization of a general complex dynamical network

Automatica (Journal of IFAC)

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Abstract

In this letter, we provide a simply approximate formula for estimating the detailed number of pinning nodes and a novel pinning synchronization criteria are obtained for a given general complex dynamical network. By using eigenvalues of the minor matrix of inner-coupling matrix and Schur lemma, we can reduce the gain factor of the controller. Previous results about symmetric coupling matrix are included as special cases of the present work. Finally a network example consists of 10 identical Lorenz systems are given to show the effectiveness of the proposed synchronization criteria.