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Anti-Control of Chaos in Fractional Difference Equations

[+] Author Affiliations
Changpin Li, Li Ma, Huang Xiao

Shanghai University, Shanghai, China

Paper No. DETC2013-12835, pp. V004T08A027; 9 pages
doi:10.1115/DETC2013-12835
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME

abstract

Fractional difference equations, or fractional maps, appear at least in two ways. One way is that some of them directly come from the discrete dynamical process with memory or heredity. Another one is that some of them are originated from the discretization of the continuous fractional differential equations. Such maps may be not chaotic. On the other hand, anti-control of chaos (or chaotification for brevity) has potential applications in secure communication. In this paper, we make non-chaotic fractional maps chaotic by constructing suitable controllers. The presented control technique and method has been applied to the non-chaotic fractional Tent map, Hénon map, and Lozi map, which become chaotic via the designed controllers. The computer graphics are also displayed to show the efficiency of the designed controllers.

Copyright © 2013 by ASME
Topics: Chaos

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