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Journal of Applied Mathematics
Volume 2014, Article ID 742956, 9 pages
http://dx.doi.org/10.1155/2014/742956
Research Article

Adaptive Synchronization of Complex Networks with Mixed Probabilistic Coupling Delays via Pinning Control

School of Electronics Information Engineering, Taiyuan University of Science and Technology, Shanxi 030024, China

Received 26 February 2014; Accepted 22 June 2014; Published 15 July 2014

Academic Editor: Qing-Wen Wang

Copyright © 2014 Jian-An Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of synchronization for a class of complex networks with probabilistic time-varying coupling delay and distributed time-varying coupling delay (mixed probabilistic time-varying coupling delays) using pinning control is investigated in this paper. The coupling configuration matrices are not assumed to be symmetric or irreducible. By adding adaptive feedback controllers to a small fraction of network nodes, a low-dimensional pinning sufficient condition is obtained, which can guarantee that the network asymptotically synchronizes to a homogenous trajectory in mean square sense. Simultaneously, two simple pinning synchronization criteria are derived from the proposed condition. Numerical simulation is provided to verify the effectiveness of the theoretical results.