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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 484039, 11 pages
Research Article

Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

School of Automation, Southeast University, Nanjing 210096, China

Received 26 May 2014; Revised 5 September 2014; Accepted 10 September 2014; Published 26 November 2014

Academic Editor: Manuel De la Sen

Copyright © 2014 Xiaomin Tian. 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.


The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.