Balancing with reflex delay

We consider the simplest possible model describing the "man-machine" system when somebody places the end of a stick on his fingertip, and tries to mov e the lowest point of the stick in a way that its upper position should be stable. The stability analysis of the mechanical model provides surprisingl y simple and dear results in spite of the fact that modelling the time dela y makes the corresponding differential equation infinite dimensional in mat hematical sense. The calculated critical delay of reflexes and the frequenc y of the nonlinear vibrations arising as a result of a Hopf bifurcation at the limit of linear stability shows good agreement with experimental observ ations. By means of the above results, we also get some in-view into the wo rk of the organ called "labyrinthus" in the inner ear which helps in self-b alancing of the human body even when our eyes are closed. (C) 2000 Elsevier Science Ltd. All rights reserved.