Periodic Flows to Chaos in Time-delay Systems

  • Albert C. J. Luo

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 16)

Table of contents

  1. Front Matter
    Pages i-x
  2. Albert C. J. Luo
    Pages 1-33
  3. Albert C. J. Luo
    Pages 35-79
  4. Albert C. J. Luo
    Pages 81-113
  5. Albert C. J. Luo
    Pages 115-155
  6. Albert C. J. Luo
    Pages 157-195
  7. Back Matter
    Pages 197-198

About this book


This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems.

  • Facilitates discovery of analytical solutions of nonlinear time-delay systems;
  • Illustrates bifurcation trees of periodic motions to chaos;
  • Helps readers identify motion complexity and singularity;
  • Explains procedures for determining stability, bifurcation and chaos.


Time-delay systems Generalized harmonic balance method Stability and bifurcations Periodic motions to chaos Quasi-periodic motions Bifurcation trees Analytical solutions in time delay systems

Authors and affiliations

  • Albert C. J. Luo
    • 1
  1. 1.Dept Mechanical & Industrial EnggSouthern Illinois Univ, Sch of Engg Dept Mechanical & Industrial EnggEdwardsvilleUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-42663-1
  • Online ISBN 978-3-319-42664-8
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site