Fractal basin boundaries and intermittency in the driven damped pendulum

We numerically study intermittency associated with the coexistence of multiple attractors in the damped, driven pendulum. For some ranges of the control parameters the basins of attraction for attractors with positive and negative average angular velocities are intricately interwoven, and the boundary between basins is a fractal set. We observe intrinsic intermittency due to a crisis, in which two chaotic attractors collide with the fractal boundary that divides their basins of attraction. For control parameters near the crisis, the fractal dimension of the basin boundaries approaches that of the phase space, and a random external forcing torque easily induces extrinsic intermittency. Both noise- and crisis-induced intermittency can produce power spectra S(ω)∝1/${\omega }^{\alpha }$, with αapeq21, over several decades in frequency ω.