STOCHASTIC MANIFESTATION OF CHAOS

We use Floquet theory to study the dynamical properties of a Fokker-Planck equation with time-dependent coefficients describing a nonlinear Brownian rotor driven by a time-periodic angle-dependent external force consisting of two traveling sine waves with amplitudes 1 and 2. For the case 2=0, the Fokker-Planck equation is separable (in the sense that it has two well-defined eigen-numbers), and the nearest-neighbor spacing distribution appears to be Poisson random for large 1. For both 10 and 20, we find evidence of nonlinear resonance and level repulsion in the Floquet spectrum and first-passage time, and the spectrum exhibits level repulsion and universal random matrix-type behavior. The long-time state is quasiperiodic in time and angle and is affected by an increasing number of modes of the system as the external field amplitude is increased. © 1990 The American Physical Society.