The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In the case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity or the mean escape time, respectively. For the problem of a fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows us to describe the structures of motion in more detail. Most complexity measures indicate the value of the correlation time at which the phenomenon of resonant activation occurs with an extremum.
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Witt et al. (1997) studied this question.
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