A Generalized Model of Active Media With a Set of Interacting Pacemakers: Application to the Heart Beat Analysis

Abstract

We propose a quite general model of active media by consideration 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 stimulater. The behavior of such a system is analyzed. Second, the microscopic level corresponding to the representation of cardiac nodes by one-and 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.

Globally attracting synchrony in a network of oscillators with all-to-all inhibitory pulse coupling

“…The synchronization tendencies of networks of oscillators have been studied intensely in the context of fireflies [1], cardiac cells [2–4], Josephson junctions [5], laser arrays [6], chemical oscillators [7], hybrid dynamical systems [8], pulse-coupled sensor networks [9], neural networks [10], and neutrino flavor oscillations [11]. There are three general approaches to studying synchronization of oscillators [12]: one can assume a form for the oscillator and for the nature of the coupling and derive results for that particular system, or one can use phase resetting theory with the assumption that the coupling is weak, or phase resetting theory with the assumption that the coupling is pulsatile.…”

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

“…In the present paper, we also utilize a well-known method for studying pulse coupled oscillators, the method of phase response curves (PRC). 28,[35][36][37][38][39] The phase response curves were first introduced and later widely used in the research devoted to oscillations in biological systems such as cardiac cells, firefly populations, and especially neural networks. Recently this method was applied to chemical oscillators with pulsatile coupling.…”