Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 105309, 15 pages
doi:10.1155/2010/105309
Research Article

Parameters Identification and Synchronization of Chaotic Delayed Systems Containing Uncertainties and Time-Varying Delay

Zhongkui Sun1,2 and Xiaoli Yang3

1Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
2Department of Physics, University of Potsdam, Postfach 601553, 14415 Potsdam, Germany
3College of Mathematics and Information Science, Shaan'xi Normal University, Xi'an 710062, China

Received 30 December 2009; Revised 5 March 2010; Accepted 24 March 2010

Academic Editor: Jerzy Warminski

Copyright © 2010 Zhongkui Sun and Xiaoli Yang. 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

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme.