Dynamical Systems Modeling and Analysis

  1. Applications in Biology
    1. Population Dynamics
      1. Single Species Models
        1. Exponential Growth
          1. Logistic Growth
            1. Allee Effects
            2. Predator-Prey Systems
              1. Lotka-Volterra Model
                1. Modifications and Extensions
                  1. Stability Analysis
                  2. Competition Models
                    1. Competitive Exclusion
                      1. Coexistence Conditions
                      2. Metapopulation Models
                        1. Patch Dynamics
                          1. Migration Effects
                        2. Epidemiology
                          1. SIR Models
                            1. Basic Reproduction Number
                              1. Epidemic Thresholds
                                1. Vaccination Strategies
                                2. SEIR Models
                                  1. Latent Period Effects
                                    1. Disease Progression
                                    2. Spatial Spread Models
                                      1. Reaction-Diffusion Equations
                                        1. Traveling Waves
                                      2. Neuroscience
                                        1. Single Neuron Models
                                          1. Integrate-and-Fire Model
                                            1. Hodgkin-Huxley Model
                                              1. FitzHugh-Nagumo Model
                                              2. Neural Networks
                                                1. Coupled Oscillators
                                                  1. Synchronization
                                                    1. Network Dynamics
                                                  2. Ecology
                                                    1. Food Web Dynamics
                                                      1. Ecosystem Stability
                                                        1. Spatial Patterns

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                                                      10. Numerical Methods and Computational Analysis

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                                                      12. Applications in Physics and Engineering