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Mathematical Problems in Engineering
Volume 2014, Article ID 808375, 10 pages
Research Article

Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

1Department of Mathematics, Umm Al-Qura University, P.O. Box 14949, Makkah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
3College of Applied Medical Sciences, Taif University, P.O. Box 21955, Turabah, Saudi Arabia

Received 5 November 2013; Revised 18 January 2014; Accepted 2 February 2014; Published 8 April 2014

Academic Editor: Kwok-Wo Wong

Copyright © 2014 Kholod M. Abualnaja and Emad E. Mahmoud. 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 main aim of this research is to find an analytical and numerical study to investigate the projective synchronization of two identical or nonidentical chaotic complex nonlinear systems with uncertain parameters. The secure communication between these systems is achieved based on this study. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve projective synchronization of chaotic attractors of these systems. The projective synchronization of two identical complex Chen systems and two different chaotic complex Lü and Lorenz systems is taken as two examples to verify the feasibility of the presented scheme. These chaotic complex systems appear in several applications in physics, engineering, and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results. The above results will provide theoretical foundation for the secure communication applications based on the proposed scheme.