Physics nonlinear ODE example for numerical methods project?

[fletch-j]

I am doing a little research project into numerical methods of solving ODEs where I do 1 half of learning about the basics of numerical methods and then look at a particular method (Linear multistep) and then the second half is looking at a particular example, applying what I've learned and writing a report about it.
I've just about completed the first part.

I was wondering if anyone could give an interesting non-linear example which I might be able to work on, or instruct me how I could find such an example and the required equation/s.
I have done a semester course on ODEs and semester of physics, and I am interested in plasma physics in the future (but I have been advised that using a specific example from plasma physics might be too unwieldy with my limited experience).

 

[Filip Larsen]

I've always been fond of the Lorenz equations [1], but there are also simple but interesting systems like the Rössler attractor [2] and Chua's circuit [3].

[1] http://en.wikipedia.org/wiki/Lorenz_system
[2] http://en.wikipedia.org/wiki/Rössler_attractor
[3] http://en.wikipedia.org/wiki/Chua's_circuit