Special thanks to the Mellon grant for funding this project.
Maple can generate graphs of chaotic systems, but it is an extremely computationally intensive task.
We will consider Duffing's Equation, which is a system of DE's in two state variables, with time acting as a third. The top end of the steel beam is attached to a rigid frame which is pulsating sinusoidally, and the bottom end is hanging just above two magnets. We must be careful how we choose to view the numerical approximations to trajectories of this system. It seems as though the resolution is too low, since points are pretty far apart. Suddenly we have a much clearer graph.