DRIVEN CHAOTIC MOTION IN SINGLE-WELL AND DOUBLE-WELL POTENTIALS

The stochastic motions in stable and bistable potentials are compared on the basis of a Langevin-like equation with a deterministic (chaotic ) process replacing Gaussian white noise. Ergodic and mixing propertie s are obtained under rather general circumstances. In the case of the symmetric double-well potential, the system exhibits a behavior, quite different from what one observes for stable potentials: as the contro l parameters are varied, the system undergoes a phase transition from an ergodic to a nonergodic phase. Lyapunov exponents and fractal dimen sions are studied for more detailed insight.