Dynamical Systems Modeling and Analysis

  1. One-Dimensional Continuous Systems
    1. Basic Framework
      1. The Equation x' = f(x)
        1. Geometric Interpretation
          1. Solution Existence
          2. Fixed Points
            1. Definition and Calculation
              1. Graphical Identification
                1. Physical Interpretation
                2. Stability Analysis
                  1. Linear Stability
                    1. Derivative Test
                      1. Stability Criteria
                      2. Nonlinear Stability
                        1. Lyapunov Stability
                          1. Basin of Attraction
                        2. Phase Line Analysis
                          1. Construction of Phase Lines
                            1. Flow Direction
                              1. Equilibrium Classification
                              2. Graphical Methods
                                1. Plotting f(x) versus x
                                  1. Identifying Flow Patterns
                                    1. Sketching Solutions
                                    2. Potential Functions
                                      1. Definition and Construction
                                        1. Relationship to Dynamics
                                          1. Energy Interpretation
                                          2. Applications
                                            1. Population Growth Models
                                              1. Chemical Kinetics
                                                1. Mechanical Systems

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                                              3. Modeling with Dynamical Systems

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                                              5. One-Dimensional Discrete Systems