1 Introduction
  1.1 A Brief History
  1.2 Book Layout
  References
2 Nonlinear Discrete Systems
  2.1 Definitions
  2.2 Fixed Points and Stability
  2.3 Stability Switching Theory
  2.4 Bifurcation Theory
  References
3 Discretization of Continuous Systems
  3.1 Continuous Systems
  3.2 Basic Discretization
    3.2.1 Forward Euler's Method
    3.2.2 Backward Euler's Method
    3.2.3 Trapezoidal Rule Discretization
    3.2.4 Midpoint Method
  3.3 Introduction to Runge-Kutta Methods
    3.3.1 Taylor Series Method
    3.3.2 Runge-Kutta Method of Order 2
  3.4 Explicit Runge-Kutta Methods
    3.4.1 Runge-Kutta Method of Order 3
    3.4.2 Runge-Kutta Method of Order 4
  3.5 Implicit Runge-Kutta Methods
    3.5.1 Polynomial Interpolation
    3.5.2 Implicit Runge-Kutta Methods
    3.5.3 Gauss Method
    3.5.4 Radau Method
    3.5.5 Lobatto Method
    3.5.6 Diagonally Implicit RK Methods
    3.5.7 Stability of Implicit Runge-Kutta Methods.
  3.6 Multi-step Methods
    3.6.1 Adams-Bashforth Methods
    3.6.2 Adams-Moulton Methods
    3.6.3 Explicit Adams Methods
    3.6.4 Implicit Adams Methods
    3.6.5 General Forms
  3.7 Generalized Implicit Multi-step Methods
  References
4 Implicit Mapping Dynamics
  4.1 Single-Step Implicit Maps
  4.2 Discrete Systems with Multiple Maps
  4.3 Complete Dynamics of a Henon Map System
  4.4 Multi-step Implicit Maps
5 References.
  Periodic Flows in Continuous Systems
  5.1 Continuous Nonlinear Systems
  5.2 Continuous Time-Delay Systems
    5.2.1 Interpolated Time-Delay Nodes
    5.2.2 Integrated Time-Delay Nodes
  5.3 Discrete Fourier Series
6 References
  6 Periodic Motions to Chaos in Duffing Oscillator
  6.1 Period- 1 Motions
  6.2 Period-m Motions
  6.3 Bifurcation Trees of Periodic Motions
  6.4 Frequency-Amplitude Characteristics
    6.4.1 Period-1 Motions to Chaos
    6.4.2 Period-3 Motions
  6.5 Numerical Simulations
  Reference
Index