Transition from chaotic to nonchaotic behavior in randomly driven systems

We discuss the explicit dependence of the final trajectory on initial conditions for randomly driven nonlinear dynamical systems which are stopped and restarted with random velocities at regular intervals (a Brownian-type motion). We find a transtion from chaotic behavior for long intervals between stops to nonchaotic behavior for short intervals between stops. For short intervals, the Lyapunov exponent is related to the thermal average square force due to the potential. The consequences for ‘‘hybrid molecular-dynamics Monte Carlo’’ sampling methods are discussed.