Dynamical Systems Modeling and Analysis

  1. Bifurcation Theory
    1. Fundamental Concepts
      1. Definition of Bifurcations
        1. Bifurcation Parameters
          1. Bifurcation Points
            1. Bifurcation Diagrams
              1. Construction Methods
                1. Interpretation
              2. Local Bifurcations in One Dimension
                1. Saddle-Node Bifurcation
                  1. Normal Form
                    1. Bifurcation Diagram
                      1. Physical Examples
                      2. Transcritical Bifurcation
                        1. Normal Form
                          1. Symmetry Properties
                          2. Pitchfork Bifurcation
                            1. Supercritical Case
                              1. Normal Form
                                1. Stability Analysis
                                2. Subcritical Case
                                  1. Normal Form
                                    1. Hysteresis Effects
                                3. Local Bifurcations in Two Dimensions
                                  1. Hopf Bifurcation
                                    1. Supercritical Hopf
                                      1. Limit Cycle Emergence
                                        1. Stability Analysis
                                        2. Subcritical Hopf
                                          1. Unstable Limit Cycles
                                            1. Hysteresis
                                          2. Saddle-Node Bifurcations in 2D
                                            1. Transcritical Bifurcations in 2D
                                              1. Pitchfork Bifurcations in 2D
                                              2. Global Bifurcations
                                                1. Homoclinic Bifurcations
                                                  1. Homoclinic Orbits
                                                    1. Bifurcation Mechanisms
                                                    2. Heteroclinic Bifurcations
                                                      1. Heteroclinic Connections
                                                        1. Cycle Formation
                                                        2. Saddle-Node of Limit Cycles
                                                          1. Blue Sky Bifurcations
                                                          2. Bifurcation Analysis Methods
                                                            1. Continuation Methods
                                                              1. Normal Form Theory
                                                                1. Center Manifold Theory

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                                                              9. Chaos Theory