Abstract
For a periodically kicked Brownian particle a noisy two-dimensional map representing the dynamics in periods of the kicks is derived. In the limits of small noise and large friction the stationary behavior is discussed in terms of the invariant density in configuration space. Particular emphasis is laid on one-dimensional bistable symmetric maps which have locally stable fixed points separated by an unstable fixed point. The rate of transitions between these points caused by weak multiplicative Gaussian white noise is determined by means of a discrete time version of Kramers’ flux over population method. The resulting rate expression is asymtotically exact for small noise and agrees very well with numerical results.
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