Behavior of a nonlinear resonator driven at subharmonic frequencies.

Abstract

We have experimentally investigated the behavior of a driven nonlinear electrical resonator over a large region of its control parameter space. If one regards the various responses of the resonator as different ``phases'' and constructs a ``phase diagram'' in the system control parameter space, many intriguing regularities become apparent. At drive frequencies far below the system's resonant frequency, there exists a series of regions which are bounded by contours that mark the successive bifurcations in a period-doubling route to chaos. There are geometrical regularities in the size and location of these regions, and we suggest empirical scaling laws to describe these features. The appearance of period doubling and chaos in nonlinear systems that are driven far below resonance can have considerable practical significance and, in the empirical observations that are given in this paper, are a step in understanding the global parameter-space behavior of nonlinear systems.