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Regularity and Complexity in Dynamical Systems

  • Book
  • © 2012

Overview

Authors:
  1. Albert C. J. Luo

    1. Edwardsville, School of Engineering, Southern Illinois University, Edwardsville, USA

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  • Illustrates new concepts and methodology in discontinuous dynamical systems
  • Uses different ideas to describe complicated dynamical systems in real worlds
  • Discusses the mechanism of chaos and diffusion in impulsive systems
  • Discusses strange attractor fragmentation and hidden mathematical structures
  • Contains intuitive illustrations and systematical description
  • Has complete example demonstrations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 1)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
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  2. Nonlinear Continuous Dynamical Systems

    • Albert C. J. Luo
    Pages 1-63

  3. Nonlinear Discrete Dynamical Systems

    • Albert C. J. Luo
    Pages 65-136

  4. Chaos and Multifractality

    • Albert C. J. Luo
    Pages 137-167

  5. Complete Dynamics and Synchronization

    • Albert C. J. Luo
    Pages 169-221

  6. Switching Dynamical Systems

    • Albert C. J. Luo
    Pages 223-296

  7. Mapping Dynamics and Symmetry

    • Albert C. J. Luo
    Pages 297-363

  8. Back Matter

    Pages 365-497
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Keywords

About this book

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Reviews

From the reviews:

“The aim of this book is to provide a basis and a survey of the main topics the author’s research is devoted to. … The first and second chapters of the book contain the nonlinear counterpart of the theory for continuous and discrete dynamical systems. … These two first chapters together with the two appendices conform a textbook for an undergraduate student.” (Maite Grau, Zentralblatt MATH, Vol. 1253, 2013)

Authors and Affiliations

  • Edwardsville, School of Engineering, Southern Illinois University, Edwardsville, USA

    Albert C. J. Luo

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