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Synchronization of Integral and Fractional Order Chaotic Systems

A Differential Algebraic and Differential Geometric Approach With Selected Applications in Real-Time

  • Rafael Martínez-Guerra
  • Claudia A. Pérez-Pinacho
  • Gian Carlo Gómez-Cortés

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 1-31
  3. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 33-42
  4. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 43-62
  5. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 63-100
  6. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 101-110
  7. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 111-124
  8. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 125-133
  9. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 135-151
  10. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 153-162
  11. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 163-174
  12. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 175-186
  13. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 187-202
  14. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 203-218
  15. Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho, Gian Carlo Gómez-Cortés
    Pages 219-236
  16. Back Matter
    Pages 237-242

About this book

Introduction

This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only basic knowledge of integer ordinary and fractional ordinary differential equations. Design applications are illustrated with the help of several physical models of practical interest.

Keywords

Algebraic and Geometric Methods in Control Theory Fractional Derivatives and Fractional Order Systems General Synchronization in Dynamical Feedback Systems Reduced-order Observers in Nonlinear Systems Secure Communication and Chaos Theory Synchronization, anti- & Multisynchronization in Chaotic Sys.

Authors and affiliations

  • Rafael Martínez-Guerra
    • 1
  • Claudia A. Pérez-Pinacho
    • 2
  • Gian Carlo Gómez-Cortés
    • 3
  1. 1.Departamento de Control AutomaticoCINVESTAV-IPNMexico, D.F.Mexico
  2. 2.Departamento de Control AutomaticoCINVESTAV-IPNMexico, D.F.Mexico
  3. 3.Departamento de Control AutomaticoCINVESTAV-IPNMexico, D.F.Mexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15284-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-15283-7
  • Online ISBN 978-3-319-15284-4
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site