Universal properties at the onset of chaos in diode resonator systems

Measurements of scaling behavior at the onset of chaos, including the ``singularity spectrum,'' or f({α}) spectrum, and the fractal dimension D of the quasiperiodic orbit set along the critical transition line, are reported for driven diode resonator systems. A single diode resonator is used for the transition to chaos through the period-doubling scenario. The system of two coupled diode resonators can be driven to exhibit quasiperiodicity and chaos. The second frequency is determined by the system but can be adjusted to give a winding number approximated by the continued fraction 〈4111. . . 〉 to an accuracy of 10^-6. The fractal dimension D is measured to be 0.87±{}0.01, in agreement with sine-circle map theory. Measured f({α}) spectra are compared with those calculated for the circle map (for the quasiperiodic route) and the logistics map (for the period-doubling route). For the quasiperiodic route, f({α}) spectra were also obtained for sub- and supercritical orbits. Good agreement with theory is found in all cases, providing experimental evidence for the universality of scaling properties at criticality within certain classes of nonlinear-dynamical systems.