Nonlinear Dynamics and Chaos

  1. Computational Methods
    1. Numerical Integration
      1. Runge-Kutta Methods
        1. Adaptive Step Size
          1. Symplectic Integrators
            1. Error Analysis
            2. Bifurcation Analysis Software
              1. AUTO
                1. MATCONT
                  1. PyDSTool
                  2. Chaos Detection Algorithms
                    1. Lyapunov Exponent Calculation
                      1. Poincaré Section Construction
                        1. Fractal Dimension Estimation
                        2. Visualization Techniques
                          1. Phase Portrait Generation
                            1. Bifurcation Diagram Construction
                              1. Attractor Visualization
                                1. Time Series Plotting

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                              18. Applications in Economics and Social Sciences

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                              1. Introduction to Dynamical Systems