550.391 Dynamical Systems
Fall 2005
- Creating Phase Portraits
Go here to download MATLAB code for phase portraits. (The file will have a name like pplane*.m)
- Runge Kutta Method
Examples
MATLAB code for skydiver and
lunar lander problems.
- Ruling Out Closed Orbits
This handout lists the theorems discussed
in class that are not in the text.
- The Lienard Plane
This handout provides another example
of Relaxation Oscillations, Lienard Systems, and working with the
Lienard Plane.
- Perturbation Theory
This handout provides a more complete
discussion of perturbation theory.
- Bifurcations in Higher Dimensions
This handout provides examples of
supercritical, subcritical, and degenerate. There is also
an example of a bistable system.
This handout provides a
clearer example of a subcritical Hopf Bifurcation than the one
presented in the previous document. (See Example 8.2.1
for an analysis of this system.)