© 2017

Memorized Discrete Systems and Time-delay


  • Introduces memorized discrete systems (MDS)

  • Provides a systematic method for MDS and applications to time-delay systems

  • Discusses MDS in connection to periodic motions to chaos


Part of the Nonlinear Systems and Complexity book series (NSCH, volume 17)

Table of contents

  1. Front Matter
    Pages i-x
  2. Albert C. J. Luo
    Pages 1-50
  3. Albert C. J. Luo
    Pages 51-114
  4. Albert C. J. Luo
    Pages 115-220
  5. Albert C. J. Luo
    Pages 221-270
  6. Albert C. J. Luo
    Pages 271-296
  7. Back Matter
    Pages 297-298

About this book


This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems.

The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.


Memorized discrete systems Discretization of time-delay systems Stability and bifurcations Periodic motions to chaos Bifurcation trees Nonlinear time-delay systems

Authors and affiliations

  1. 1.Department of Mechanical and Industrial Engineering, School of EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA

About the authors

Professor Albert C.J. Luo is Professor of Mechanical Engineering at the University of Southern Illinois, Edwardsville.

Bibliographic information

Industry Sectors
Oil, Gas & Geosciences


“This monograph is devoted to the study of discrete dynamical systems with memory. It gives a comprehensive presentation of methods that have been developed for time-delay systems which can be discretized into the memorized discrete dynamical systems.” (Anatoly Martynyuk, zbMATH 1408.93001, 2019)