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Complexity
Volume 2017 (2017), Article ID 9189120, 17 pages
https://doi.org/10.1155/2017/9189120
Research Article

Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems

1Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt
2Nanoelectronics Integrated Systems Center, Nile University, Cairo 12588, Egypt

Correspondence should be addressed to Ahmed G. Radwan

Received 30 July 2016; Accepted 16 November 2016; Published 16 February 2017

Academic Editor: Michael Small

Copyright © 2017 Wafaa S. Sayed et al. 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

This paper proposes a novel generalized switched synchronization scheme among fractional-order chaotic systems with various operating modes. Digital dynamic switches and dynamic scaling factors are employed, which offer many new capabilities. Dynamic switches determine the role of each system as a master or a slave. A system can either have a fixed role throughout the simulation time (static switching) or switch its role one or more times (dynamic switching). Dynamic scaling factors are used for each state variable of the master system. Such scaling factors control whether the master is a single system or a combination of several systems. In addition, these factors determine the generalized relation between the original systems from which the master system is built as well as the slave system(s). Moreover, they can be utilized to achieve different kinds of generalized synchronization relations for the purpose of generating new attractor diagrams. The paper presents a mathematical formulation and analysis of the proposed synchronization scheme. Furthermore, many numerical simulations are provided to demonstrate the successful generalized switched synchronization of several fractional-order chaotic systems. The proposed scheme provides various functions suitable for applications such as different master-slave communication models and secure communication systems.