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Understanding Complex Systems

Advances in Synchronization of Coupled Fractional Order Systems

Fundamentals and Methods

Authors: Martínez-Guerra, Rafael, Pérez-Pinacho, Claudia Alejandra

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  • Provides a self-contained account on recent advances in fractional order dynamical systems
  • Contains a lot of introductory and background material, as well as worked examples for newcomers to the field
  • Offers a special chapter on secure communications as newly emerging topic for fractional order systems modeling
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eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-93946-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-93945-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-3-030-06752-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering.

As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few.

This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems. 


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Pages 1-10

    Martínez-Guerra, Rafael (et al.)

  • Basic Concepts and Preliminaries

    Pages 11-39

    Martínez-Guerra, Rafael (et al.)

  • Synchronization of Chaotic Systems by Means of a Nonlinear Observer: An Application to Secure Communications

    Pages 41-49

    Martínez-Guerra, Rafael (et al.)

  • Synchronization for Chaotic System Through an Observer Using the Immersion and Invariance (I&I) Approach

    Pages 51-60

    Martínez-Guerra, Rafael (et al.)

  • Synchronization of Nonlinear Fractional-Order Systems by Means of PI$$^{r\alpha }$$ Reduced Order Observer

    Pages 61-70

    Martínez-Guerra, Rafael (et al.)

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-319-93946-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-93945-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-3-030-06752-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Synchronization of Coupled Fractional Order Systems
Book Subtitle
Fundamentals and Methods
Authors
Series Title
Understanding Complex Systems
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-93946-9
DOI
10.1007/978-3-319-93946-9
Hardcover ISBN
978-3-319-93945-2
Softcover ISBN
978-3-030-06752-6
Series ISSN
1860-0832
Edition Number
1
Number of Pages
XIX, 185
Number of Illustrations
7 b/w illustrations, 59 illustrations in colour
Topics