On-off intemittency phenomena in a pendulum with a randomly vibrating suspension axis

We demonstrate that the excitation of noise-induced oscillations of a pendulum with a randomly vibrating suspension axis occurs via ‘on-off intermittency’. The dependence of the mean duration of ‘laminar’ phase on the excess of the noise intensity over a certain critical value is calculated analytically. These theoretical dependencies are confirmed by the results of numerical experiments. Further, we study the influence of an additional harmonic action. It is shown that the oscillations are intensified if the frequency of this action is low, and suppressed if the action frequency is high. It is interesting that the suppression of the oscillations, much like their excitation, occurs via ‘on-off intermittency’. The dependence of the mean duration of ‘laminar’ phase on the action amplitude is obtained from numerical experiments.