Page 329 - Mathematical Techniques of Fractional Order Systems

Chapter 11

Multiswitching Synchronization

of Commensurate Fractional
Order Hyperchaotic Systems

Via Active Control

1
4
2,3
Shikha Singh , Ahmad Taher Azar , Sundarapandian Vaidyanathan ,
5
Adel Ouannas and Muzaffar A. Bhat 1
1 2
Jamia Millia Islamia, New Delhi, India, Faculty of Computers and Information, Benha
3
University, Benha, Egypt, School of Engineering and Applied Sciences, Nile University, Giza,
5
4
Egypt, Vel Tech University, Chennai, Tamil Nadu, India, University of Larbi Tebessi,
Tebessa, Algeria
11.1 INTRODUCTION
Almost three centuries have passed since the emergence of fractional calculus.
The major merit of fractional calculus, different from integer calculus, lies in
the fact that the fractional order system describes real systems in interdisciplin-
ary fields more elegantly in comparison to the integer order system, as it has
memory, and has proven to be a very suitable tool for the description of mem-
ory and hereditary properties of various materials and processes (Lyapunov,
1992). During this time many researchers have devoted a lot of time and
energy to reveal the investigations on fractional derivatives in detail (Li and
Deng, 2007). Among the wide range of studies that have been done in this
direction, it has been observed that some of the fractional order differential
systems display chaotic behavior (Petras, 2011; El-Sayed et al., 2016;
Tolba et al., 2017). Tavazoei and Haeri (2009) suggested two techniques for
detecting chaotic properties in a class of fractional order systems. Various
researchers have focused to develop the efficient and robust schemes of syn-
chronization and control of chaotic systems. With the evolution of models
based on fractional order differential systems the chaos synchronization and
chaos control in fractional order chaotic systems are becoming important
emerging areas of research. During the studies on the chaos synchronization
and chaos control in fractional order chaotic systems it has been observed, that

Mathematical Techniques of Fractional Order Systems. DOI: https://doi.org/10.1016/B978-0-12-813592-1.00011-8
© 2018 Elsevier Inc. All rights reserved. 319