Stick balancing: On-off intermittency and survival times

The ∞uctuations in the vertical displacement angle of a stick balanced at the flngertip exhibit on-ofi intermitency. However, even a skilled balancer cannot indeflnitely maintain a stick balanced at their flngertip. The survival function for stick balancing, P(tesc > t), is shown to have the form of a Weibul function, exp(i‚t) fl , where ‚ is a constant and fl > 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.

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