Concept of Dynamical Traps: Model Systems of Human Actions and Experimental Evidence

Abstract

Dynamical traps as a new emergence mechanism related to the bounded capacity of human cognition is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. This is described in terms of some neighborhood of the equilibrium point, the region of dynamical traps, wherein each point is regarded as an equilibrium one by the operators. So when a system enters this region and while it is located in it, maybe for a long time, the operator control is suspended. A simple model of oscillator with dynamical traps and the characteristic features of its dynamics are discussed. Experiments on the balancing of a virtual pendulum were conducted to examine the basic features of human control over unstable systems that are expected to be affected by human fuzzy rationality. It is demonstrated that practically only the dimensions of the phase space region wherein a given pendulum trajectory is located depend on the subject age and skill as well as the pendulum parameters determining the difficulty of the balancing. In contrast, the forms of the distribution functions are the same for all the subjects. The data of the virtual experiments are compared to the results of numerical simulation of the oscillator with dynamical traps. The phase trajectories and the phase variable distributions are shown to be similar for the two systems. In addition a chain of oscillators with dynamical traps which mimics cooperative interaction of human operators is considered also. It is, actually, demonstrated that the human fuzzy rationality can cause complex cooperative dynamics in many-element ensembles.