© 2015

Discretization and Implicit Mapping Dynamics


Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Albert C. J. Luo
    Pages 1-9
  3. Albert C. J. Luo
    Pages 11-50
  4. Albert C. J. Luo
    Pages 51-158
  5. Albert C. J. Luo
    Pages 159-197
  6. Albert C. J. Luo
    Pages 199-279
  7. Albert C. J. Luo
    Pages 281-307
  8. Back Matter
    Pages 309-310

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.


Chaos Duffing Oscillator Discretization Continuous Systems Discretization-Implicit Mapping Dynamics- Implicit Mapping Dynamics Nonlinear Discrete Systems Periodic Flows and Chaos-Bifurcation Trees to Chaos-Discrete Fourier Series

Authors and affiliations

  1. 1.Department of Mechanical and Industrial EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA

About the authors

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