Double Poincaré sections of a quasi-periodically forced,chaotic attractor

A nonlinear mechanical oscillator is forced with two incommensurate harmonic signals and chaotic vibrations are experimentally observed. The fractal nature of this strange attractor in four-dimensional phase space is revealed by using a double Poincaré section. This section involves a narrow timing pulse on one harmonic driving signal and a wider phase window on the other forcing harmonic signal. The resulting two-dimensional map shows a Cantor set structure characteristic of strange attractors. The transition from quasi-periodic to chaotic vibrations is also observed.