Stick balancing: On–off intermittency and survival times

The fluctuations in the vertical displacement angle of a stick balanced at the fingertip exhibit on-off intermitency. However, even a skilled balancer cannot indefinitely maintain a stick balanced at their fingertip. The survival function for stick balancing, P (tesc > t), is shown to have the form of a Weibul function, exp(−λt)β , where λ is a constant and β > 1. The measured survival function can be reproduced by a stochastic delayed discrete map possessing only unstable solutions. These observations emphasize the importance of state–dependent, or paametric, noise in this balancing task.