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2017 | OriginalPaper | Chapter

Control and Synchronization of Fractional-Order Chaotic Systems

Authors : Ahmed G. Radwan, Wafaa S. Sayed, Salwa K. Abd-El-Hafiz

Published in: Fractional Order Control and Synchronization of Chaotic Systems

Publisher: Springer International Publishing

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Abstract

The chaotic dynamics of fractional-order systems and their applications in secure communication have gained the attention of many recent researches. Fractional-order systems provide extra degrees of freedom and control capability with integer-order differential equations as special cases. Synchronization is a necessary function in any communication system and is rather hard to be achieved for chaotic signals that are ideally aperiodic. This chapter provides a general scheme of control, switching and generalized synchronization of fractional-order chaotic systems. Several systems are used as examples for demonstrating the required mathematical analysis and simulation results validating it. The non-standard finite difference method, which is suitable for fractional-order chaotic systems, is used to solve each system and get the responses. Effect of the fractional-order parameter on the responses of the systems extended to fractional-order domain is considered. A control and switching synchronization technique is proposed that uses switching parameters to decide the role of each system as a master or slave. A generalized scheme for synchronizing a fractional-order chaotic system with another one or with a linear combination of two other fractional-order chaotic systems is presented. Static (time-independent) and dynamic (time-dependent) synchronization, which could generate multiple scaled versions of the response, are discussed.

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Title: Control and Synchronization of Fractional-Order Chaotic Systems
Authors: Ahmed G. Radwan
Wafaa S. Sayed
Salwa K. Abd-El-Hafiz
Publisher: Springer International Publishing
Book: Fractional Order Control and Synchronization of Chaotic Systems
Print ISBN: 978-3-319-50248-9

Electronic ISBN: 978-3-319-50249-6

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-50249-6_11

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