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Two-Dimensional Rotation of Chaotic Attractors: Demonstrative Examples and FPGA Realization

  • W. S. Sayed
  • A. G. RadwanEmail author
  • M. Elnawawy
  • H. Orabi
  • A. Sagahyroon
  • F. Aloul
  • A. S. Elwakil
  • H. A. Fahmy
  • A. El-Sedeek
Short Paper
  • 31 Downloads

Abstract

In this work, we demonstrate the possibility of performing two-dimensional rotation on a chaotic system. This enables the rotation of its attractor in space without changing its chaotic dynamics. In particular, the rotated system preserves the same eigenvalues at all equilibrium points and its largest Lyapunov exponent remains unchanged. Two chaotic systems, one of which is the classical Lorenz system, are used to illustrate and validate the rotation operation using numerical simulations and further experimentally using a digital FPGA platform.

Keywords

Chaotic oscillators Digital chaos generation FPGA Two-dimensional rotation 

Notes

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Engineering Mathematics and Physics Department, Faculty of EngineeringCairo UniversityGizaEgypt
  2. 2.Nanoelectronics Integrated Systems CenterNile UniversityCairoEgypt
  3. 3.Department of Computer Science and EngineeringAmerican University of SharjahSharjahUnited Arab Emirates
  4. 4.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  5. 5.Department of Electrical and Computer EngineeringUniversity of CalgaryAlbertaCanada
  6. 6.Electronics and Communications Engineering Department, Faculty of EngineeringCairo UniversityGizaEgypt

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