A GENERALIZED MODEL OF ACTIVE MEDIA WITH A SET OF INTERACTING PACEMAKERS: APPLICATION TO THE HEART BEAT ANALYSIS

Abstract

We propose a fairly general model of active media by considering of the interaction between pacemakers via their phase response curves. This model describes a network of pulse oscillators coupled by their response to the internal depolarization of mutual stimulations. First, a macroscopic level corresponding to an arbitrary large number of oscillatory elements coupled globally is considered. As a specific and important case of the proposed model, the bidirectional interaction of two cardiac nodes is described. This case is generalized by means of an additional pacemaker, which can be expounded as an external stimulator. The behavior of such a system is analyzed. Second, the microscopic level corresponding to the representation of cardiac nodes by two-dimensional lattices of pulse oscillators coupled via the nearest neighbors is described. The model is a universal one in the sense that on its basis one can easily construct discrete distributed media of active elements, which interact via phase response curves.