Math Insight

Thread: Elementary dynamical systems

Introduction to discrete and continuous dynamical systems that assumes little background. Initial discrete dynamical system material requires no calculus. The remainder assumes knowledge of differentiation but not of integration.

  1. Discrete dynamical systems 1 (no calculus required)
    1. Dynamical system introduction
    2. Some initial models
      1. An infectious disease model
      2. Controlling a rabbit population
    3. Linear models
      1. Initial bacteria growth model
      2. Penicillin clearance model
      3. Exponential growth and decay
      4. Chemical pollution
    4. Cobwebbing and stability
    5. Problems
  2. Discrete dynamical systems 2 (differentiation assumed)
    1. Stability of equilibria in discrete dynamical systems
    2. Logistic growth
    3. Problems
  3. Autonomous differential equations
    1. Introduction
    2. Solution methods
      1. Solution to linear equation
      2. Graphical methods
      3. Stability of equilibria
      4. Numerical solution
    3. Bifurcations
    4. An infectious disease model
    5. Problems
  4. Two dimensional autonomous differential equations
    1. Biological model
      1. An infectious disease model
      2. Dynamics of competition
      3. Predator-prey dynamics
      4. A spiking neuron
    2. Phase plane analysis
    3. Problems

AltStyle によって変換されたページ (->オリジナル) /