On Cellular Automata Modeling of Cardiac Pacemaker

Motivated by modern physiology, cellular automata of Greenberg-Hastings type is considered. The basic cell of the system performs a cyclic 3-state intrinsic dynamics F -> R -> A -> F -> ... which is delimited by time intervals n(F), n(R), n(A) of steps spent by the cell in particular states. It is shown that proposed cellular automata can be thought as a reliable approximate model to the real cardiac pacemaker. The time intervals determine the period of the whole pacemaker beating. The relation between n(R) and n(F) works as a switch between two types of global dynamics: active dynamics where permanent mutual impacts between cells generate the most frequent impulses, and passive dynamics which is distinguished by the special self-organization of phases between the subsequent cells. The passive dynamics allows to propagate signals from the outside world while the active dynamics protects the system against external influence.