Regularity and Complexity in Dynamical Systems

  • Albert C. J. Luo

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Albert C. J. Luo
    Pages 1-63
  3. Albert C. J. Luo
    Pages 65-136
  4. Albert C. J. Luo
    Pages 137-167
  5. Albert C. J. Luo
    Pages 169-221
  6. Albert C. J. Luo
    Pages 223-296
  7. Albert C. J. Luo
    Pages 297-363
  8. Back Matter
    Pages 365-497

About this book

Introduction

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.

This book also:

  • Illustrates new concepts and methodology in discontinuous dynamical systems
  • Uses different ideas to describe complicated dynamical systems in real worlds
  • Discuss the complete dynamics and the corresponding Ying-Yang theory as well as  complexity and factuality of chaos in dynamical systems
  • Discusses the mechanism of chaos and diffusion in impulsive systems
  • Discusses strange attractor fragmentation and hidden mathematical structures
  • Contains intuitive illustrations and systematical description as well as complete example demonstrations

Regularity and Complexity in Dynamical Systems is an ideal book for those interested in better understanding complexity and chaos caused by nonlinearity, discontinuity, switching, and impulses.

Keywords

Discontinuous dynamical systems Grazing bifurcation Impulsive systems Mapping dynamics Strange attractor fragmentation Switching systems

Authors and affiliations

  • Albert C. J. Luo
    • 1
  1. 1.Edwardsville, School of EngineeringSouthern Illinois UniversityEdwardsvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1524-4
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Engineering
  • Print ISBN 978-1-4614-1523-7
  • Online ISBN 978-1-4614-1524-4
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • About this book