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Computer simulation of stick balancing: action point analysis

We analyze data collected during the series of experiments aimed at elucidation of basic properties of human perception, namely, the limited capacity of ordering events, actions, etc. according to their preference. Previously it was shown that in a wide class of human-controlled systems small deviations from the equilibrium position do not cause any actions of the system's operator, so any point in a certain neighborhood of equilibrium position is treated as an equilibrium one. This phenomenon can be described by the notion of dynamical traps that was introduced to denote a region in the system phase space where the object under consideration cannot clearly determine the most preferable of the positions that are similar in some sense. According to this concept, the motion of the system in the dynamical trap region is mainly not affected by the operator. The moments of time when the system leaves the dynamical trap region, or in other words, when the operator decides to start or stop the control over the system, are called action points [1]. These moments are seem to be determined intuitively by the operator, and the purpose of our work is to understand the nature of such intuitive decision making process by investigating the action points data obtained from the experiments.