Duffing Dust: Poincare sections of chaos
Chaos theory is a topic that has captured the popular imagination with colorful graphics, strange attractors, the "butterfly effect", and its role in movies such as Jurassic Park. 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 equation arises when modeling a steel beam which is thin and elastic (so it can vibrate). 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. One can model this situation with the driven damped Duffing's equation:
