Nonlinear systems with fast and slow motions:changes in the probability distribution for fast motions under the influence of slower ones

摘要

The influence of slow processes on the probability distribution of fast random processes is investigated. By reviewing four examples we show that such influence is apparently of a universal character and that, in some cases, this universality is of multifractal form. As our examples we consider theoretically stochastic resonance, turbulent jets with acoustic forcing, and two problems studied experimentally by Shnoll on the influence of the Earth’s slow rotation on the probability distribution for the velocities of model Brownian particles and on alpha decay. In the case of stochastic resonance, the slow process is a low frequency, harmonic, external force. In the case of turbulent jets, the slow process is acoustic forcing. In the models based on Shnoll’s experiments, the slow processes are inertial forces arising from the rotation of the Earth, both about its own axis and about the Sun. It is shown that all of these slow processes cause changes in the probability distributions for the velocities of fast processes interacting with them, and that these changes are similar in form.