Dynamical Systems Modeling and Analysis

  1. One-Dimensional Discrete Systems
    1. Basic Framework
      1. The Map x_{n+1} = f(x_n)
        1. Iteration Process
          1. Orbit Structure
          2. Fixed Points
            1. Definition and Calculation
              1. Graphical Identification
                1. Stability Analysis
                  1. Linear Stability
                    1. Derivative Criterion
                  2. Graphical Analysis
                    1. Cobweb Plots
                      1. Construction Method
                        1. Interpretation of Dynamics
                          1. Stability Visualization
                          2. Staircase Diagrams
                          3. Periodic Orbits
                            1. Period-2 Cycles
                              1. Existence Conditions
                                1. Stability Analysis
                                2. Higher-Period Cycles
                                  1. Period-Doubling
                                    1. Stability Criteria
                                  2. Chaotic Dynamics
                                    1. Sensitive Dependence
                                      1. Aperiodic Orbits
                                        1. The Logistic Map
                                          1. Parameter Regimes
                                            1. Bifurcation Structure

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                                        4. One-Dimensional Continuous Systems

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                                        6. Two-Dimensional Linear Systems