Design of Digital Chaotic Systems Updated by Random Iterations

  • Qianxue Wang
  • Simin Yu
  • Christophe Guyeux

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Nonlinear Circuits book sub series (BRIEFSNONLINCIRC)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 1-10
  3. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 11-33
  4. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 35-45
  5. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 47-57
  6. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 59-88
  7. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 89-101
  8. Qianxue Wang, Simin Yu, Christophe Guyeux
    Pages 103-104
  9. Back Matter
    Pages 105-110

About this book


This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework for composing them. The contributors demonstrate that the associated state networks of digital chaotic systems are strongly connected. They then further prove that digital chaotic systems satisfy Devaney’s definition of chaos on the domain of finite precision. The book presents Lyapunov exponents, as well as implementations to show the potential application of digital chaotic systems in the real world; the authors also discuss the basic advantages and practical benefits of this approach. 

The authors explore the solutions to dynamic degradation (including short cycle length, decayed distribution and low linear complexity) by proposing novel modelling methods and hardware designs for two different one-dimensional chaotic systems, which satisfy Devaney’s definition of chaos. They then extend it to a higher-dimensional digital-domain chaotic system, which has been used in image-encryption technology. This ensures readers do not encounter large differences between actual and theoretical chaotic orbits through small errors. 

Digital Chaotic Systems serves as an up-to-date reference on an important research topic for researchers and students in control science and engineering, computing, mathematics and other related fields of study.


Digital Chaotic System Chaotic Encryption Circuit Implementation Dynamical Degradation FPGA Implementation Random Number Generator Devaney’s definition of chaos Lyapunov exponents

Authors and affiliations

  • Qianxue Wang
    • 1
  • Simin Yu
    • 2
  • Christophe Guyeux
    • 3
  1. 1.School of AutomationGuangdong University of TechnologyGuangzhouChina
  2. 2.School of AutomationGuangdong University of TechnologyGuangzhouChina
  3. 3.Femto-st institute, UMR 6174 CNRSUniversity of Bourgogne Franche-ComtéBesançonFrance

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-73548-1
  • Online ISBN 978-3-319-73549-8
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site
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