We explored chaos in a system that approximated the duffing oscillator through the use of a driven steel read and a pair of magnets, and observed how the strange attractor to chaos was highly dependent of some critical input parameters that caused a chaotic state in the system. Moreover, we observed that the fractal dimension of chaos was proportional derivative of the forcing function as we swept through the sampling phase. We also found that chaos presents itself in islands of chaos in the F_o – ω space, of which each island produces a unique strange attractor for a given symmetric potential. Finally, we concluded by observing that for an approximated duffing oscillator, the fractal dimension of chaos is highly depended on the magnetic separation, the symmetry of the potential wells, the sampling phase, the driving force, and the driving frequency. Observing a relationship between these variables individually and the fractal dimension of a chaos sample would require very meticulous experimentation, but could potentially lead to some interesting results.

Image of experimental setup schematic courtesy of Carnegie Mellon University's Modern Physics Laboratory Chaos Manual.