Dynamical Systems

1.	Single Differential Equations
  1.1   Population Models
          1.1.1    Population models
          1.1.2    Mathematica Computations
  1.2   The Logistic Equation and Generalizations
          1.2.1    The Logistic Equation and Generalizations
          1.1.2    Mathematica Computations
  1.3   The SI epidemic model
  1.4   Bifurcations
  1.5   Moving Objects
  1.6   Electric circuits
  1.7   Estimating Paramters in Differential Equations

2.	Single Difference Equations
  2.1   Difference Equations of the form x(n+1) = f(x(n))
          2.1.1    Concepts
          2.1.2    Mathematica Computations
  2.2   Oscillatory Solutions
          2.2.1    Oscillations in Difference Equations
          2.2.2    Mathematica Computations
  2.3   Periodic Equilibrium Solutions
          2.3.1    Concepts
          2.3.2    Mathematica Computations
  2.4   Bifurcations
          2.4.1    Concepts
          2.4.2    Logistic difference equations

3.	Linear Systems of Differential Equations
  3.1   Solving Linear Systems
          3.1.1   Solving with eigenvalues and eigenvectors
          3.1.2   Computations with Mathematica
  3.2   Equilibrium Solutions and Equilibrium Points
  3.3   Phase Portraits
          3.3.1   The phase portrait
          3.3.2   Mathematica Computations
  3.4   Complex Eigenvalues
          3.4.1   Complex Eigenvalues
          3.4.2   Mathematica computations
  3.5   Difference Equations
          3.5.1   Real Eigenvalues
          3.5.2   Complex Eigenvalues
  3.6   Repeated Eigenvalues
          3.6.1   Differential Equations
          3.6.2   Difference Equations
  3.7   Inhomogeneous Equations
          3.7.1   Undetermined Coefficients
          3.7.2   Decoupling the Equations
          3.7.3   Resonance
  3.8   Second order equations
  3.9   Compartment Models
          3.9.1   Theory
          3.9.2   Mathematica Computations
  3.10  Electrical Networks
          3.10.1  An Example
          

4.	Nonlinear Systems of Differential Equations
  4.1   Pairs of Equations
          4.1.1   General principles
          4.1.2   Numerical solution of nonlinear systems
  4.2   Equilibrium Solutions and Equilibrium Points
          4.2.1   General principles
          4.2.2   Mathematica Computations
  4.3   Nullclines
          4.3.1   General principles
          
  3.5   Trajectories and Phase Portraits
          3.5.1   The phase portrait
          3.5.2   Mathematica Computations
  4.4   The vector field { f(x,y), g(x,y) } and nullclines
  4.5   Stability and linearization
  4.6   Conservation Laws
          4.6.1   Basic Concepts
          4.6.3   A nonlinear spring magnet

5.	Examples
  5.1   The SIR epidemic model
  5.2   Glucose-Insulin kinetics
  5.3   Lienards equation
  5.4   The Belousov - Zhabotinsky equation
  5.5   A predator-prey model with a limit cycle
  5.6   Rossler's equations

  Mathematics 404 Directory