- Differential Equations: Lorenz System
Java demos of M.C. Cross (CalTech),
Pictures for logistic map
Chaos in a chemical system
- Strange attractors, Lyapunov exponents
- Logistic Map
Cobweb diagram, period-doubling cascade and chaos, Lyapunov exponents
Experiments in Rayleigh-Benard convection
- Universality and Renormalization
- Cantor Sets and Fractal Dimension
- Diagnostic Tools
Attractor reconstruction, Poincare section, power spectrum
The course uses the textbook Nonlinear Dynamics and Chaos:
With Applications to Physics, Biology, Chemistry and Engineering
by S. Strogatz.
Sketch of Course Notes Postscript
PDF (poor quality on screen, prints o.k.))
Please note, the pdf-version has poor font quality and may not be completely up to date.
Please note that the notes are still evolving while the class is progressing.
They may still have mistakes and typos: please point them out to me if you find
HW 1 PS HTML PDF
HW 2 PS HTML PDF
HW 3 PS PDF
HW 4 PS PDF
HW 5 PS PDF
HW 6 PS PDF
HW 7 PS PDF
Final PS PDF
Aitta, Ahlers, Cannell paper
If your browser does not show the html-file appropriately you may tune it by following these
Discussion section: Wednesday 5-6 in L251
The homework will be done in groups which I have
assigned. Please let me know if you are not
on that list. The homework will not be graded. Instead students
will present and explain the homework to the other students in the class
in the discussion section at the blackboard.
Ted Rieger email@example.com will lead the discussion sections.
The grade for the class will be based on the presentations (25 %) and a take-home final (75 %).
MATLAB.There are a number of tutorials and more detailed manuals of MATLAB on the web. A good starting page
is the tutorial from UMD which also
points to more detailed and extensive web resources (.e.g. the tutorial by S. Davis (Rice)). Please note that the current version of Matlab is 6 and it differs in some relevant respects from the older versions.
Template for logistic growth program:
Phaseplane program pplane5.m, ppn5out.m by J.C. Polking
Note: to get the orbits in pplane5 over longer times one can choose ode23 and pick a
calculation window that is 10 times larger than the display window.
Program for solving the Swift-Hohenberg model:
There will be no class on Tuesday October 8 and Thursday October 10.
The class will be made up in two extra sessions.
Office Hours: Mo 5-6 and Tu, Th 5-6 in
The following seminars may be of interest to students in this class:
Interdisciplinary Seminar in Nonlinear Science
on Fridays at 2pm in M416.
Graduate Student Seminar
You can subscribe to the listserver announcing the nonlinear seminars by sending
a message to esam.northwestern.edu with the subject subscribe
Both seminars are part of the IGERT Program :
Dynamics of Complex Systems in Engineering and Science