Nonlinear Dynamics and Chaos

  1. Introduction to Chaos in Continuous Systems
    1. The Lorenz System
      1. Physical Derivation from Convection
        1. Mathematical Formulation
          1. Parameter Analysis
            1. Fixed Points and Linear Stability
              1. The Lorenz Attractor
                1. Geometric Structure
                  1. Butterfly Shape
                    1. Strange Attractor Properties
                  2. Defining Chaos
                    1. Sensitive Dependence on Initial Conditions
                      1. Topological Transitivity
                        1. Dense Periodic Orbits
                          1. Aperiodicity
                            1. Deterministic vs. Stochastic Behavior
                            2. Quantifying Chaos
                              1. Lyapunov Exponents
                                1. Definition for Flows
                                  1. Calculation Methods
                                    1. Interpretation of Signs
                                      1. Lyapunov Spectrum
                                      2. Correlation Dimension
                                        1. Kolmogorov-Sinai Entropy
                                        2. Other Chaotic Systems
                                          1. Rössler System
                                            1. Chua's Circuit
                                              1. Duffing Oscillator
                                                1. Van der Pol Oscillator

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                                              4. Higher-Dimensional Systems

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                                              6. Discrete Dynamical Systems and Maps