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Discretization and Implicit Mapping Dynamics

  • Book
  • © 2015

Overview

Authors:
  1. Albert C. J. Luo

    1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, USA

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  • The first monograph to discuss the implicit mapping dynamics of periodic flows to chaos
  • Provides both explicit and implicit discrete maps of continuous systems
  • Discusses the implicit dynamics of period-m solutions in discrete nonlinear systems
  • Offers a way to find periodic flows to chaos in nonlinear systems with and without time-delay
  • Presents the discrete Fourier series of discrete nodes of periodic motion
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonlinear Physical Science (NPS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Albert C. J. Luo
    Pages 1-9

  3. Nonlinear Discrete Systems

    • Albert C. J. Luo
    Pages 11-50

  4. Discretization of Continuous Systems

    • Albert C. J. Luo
    Pages 51-158

  5. Implicit Mapping Dynamics

    • Albert C. J. Luo
    Pages 159-197

  6. Periodic Flows in Continuous Systems

    • Albert C. J. Luo
    Pages 199-279

  7. Periodic Motions to Chaos in Duffing Oscillator

    • Albert C. J. Luo
    Pages 281-307

  8. Back Matter

    Pages 309-310
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Keywords

About this book

This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics, control systems, and engineering.

Authors and Affiliations

  • Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, USA

    Albert C. J. Luo

About the author

Albert C.J. Luo is an internationally recognized professor in nonlinear dynamics and mechanics. He is a Distinguished Research Professor at Southern Illinois University Edwardsville, USA. His principal research interests lie in the fields of Hamiltonian chaos, nonlinear deformable-body dynamics, discontinuous dynamical systems, regularity and complexity in nonlinear systems, analytical and numerical solutions of differential equations.

Bibliographic Information

  • Book Title: Discretization and Implicit Mapping Dynamics

  • Authors: Albert C. J. Luo

  • Series Title: Nonlinear Physical Science

  • DOI: https://doi.org/10.1007/978-3-662-47275-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2015

  • Hardcover ISBN: 978-3-662-47274-3Published: 13 August 2015

  • Softcover ISBN: 978-3-662-51709-3Published: 23 October 2016

  • eBook ISBN: 978-3-662-47275-0Published: 30 July 2015

  • Series ISSN: 1867-8440

  • Series E-ISSN: 1867-8459

  • Edition Number: 1

  • Number of Pages: X, 310

  • Number of Illustrations: 20 b/w illustrations, 26 illustrations in colour

  • Additional Information: Jointly published with Higher Education Press, Beijing, China

  • Topics: Applications of Nonlinear Dynamics and Chaos Theory, Difference and Functional Equations, Vibration, Dynamical Systems, Control

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