Dynamical Systems Modeling and Analysis

  1. Modeling with Dynamical Systems
    1. The Modeling Process
      1. Problem Formulation
        1. Identifying System Variables
          1. Determining System Boundaries
            1. Selecting Relevant Parameters
            2. Assumption Development
              1. Simplifying Assumptions
                1. Physical Constraints
                  1. Mathematical Approximations
                  2. Equation Derivation
                    1. Conservation Laws
                      1. Constitutive Relations
                        1. Empirical Laws
                          1. Dimensional Analysis
                          2. Model Validation
                            1. Comparison with Data
                              1. Sensitivity Analysis
                                1. Parameter Estimation
                                  1. Model Refinement
                                2. Continuous-Time Modeling
                                  1. Single Variable Systems
                                    1. First-Order ODEs
                                      1. Growth and Decay Models
                                        1. Logistic Growth
                                        2. Multi-Variable Systems
                                          1. Coupled ODEs
                                            1. Vector Notation
                                              1. System Reduction Techniques
                                              2. Physical System Modeling
                                                1. Mechanical Systems
                                                  1. Electrical Circuits
                                                    1. Chemical Reactions
                                                  2. Discrete-Time Modeling
                                                    1. Difference Equations
                                                      1. Linear Difference Equations
                                                        1. Nonlinear Difference Equations
                                                          1. Solution Techniques
                                                          2. Iterated Maps
                                                            1. One-Dimensional Maps
                                                              1. Multi-Dimensional Maps
                                                                1. Population Models
                                                                  1. Economic Models

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                                                              2. Mathematical Foundations

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                                                              4. One-Dimensional Continuous Systems