Authors:
- 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
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
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.
Authors and Affiliations
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Automatic Control, CINVESTAV-IPN, Mexico City, Mexico
Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
Bibliographic Information
Book Title: Advances in Synchronization of Coupled Fractional Order Systems
Book Subtitle: Fundamentals and Methods
Authors: Rafael Martínez-Guerra, Claudia Alejandra Pérez-Pinacho
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-3-319-93946-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-93945-2Published: 06 August 2018
Softcover ISBN: 978-3-030-06752-6Published: 03 January 2019
eBook ISBN: 978-3-319-93946-9Published: 23 July 2018
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: XIX, 185
Number of Illustrations: 7 b/w illustrations, 59 illustrations in colour
Topics: Statistical Physics and Dynamical Systems, Vibration, Dynamical Systems, Control, Applications of Nonlinear Dynamics and Chaos Theory, Complexity