BIFURCATIONS IN A DISCONTINUOUS CIRCLE MAP: A THEORY FOR A CHAOTIC CARDIAC ARRHYTHMIA

Author:

BUB GIL1,GLASS LEON1

Affiliation:

1. Department of Physiology, McGill University, Montreal, Quebec Canada H3G 1Y6, Canada

Abstract

The dynamics of discontinuous circle maps are investigated in the context of modulated parasystole, a cardiac arrhythmia in which there is an interaction between normal (sinus) and abnormal (ectopic) pacemaking sites in the heart. A class of noninvertible discontinuous circle maps with slope greater than 1 displays banded chaos under certain conditions. Banded chaos in these maps is characterized by a zero rotation interval width in the presence of a positive Lyapunov exponent. The bifurcations of a simple piecewise linear circle map are investigated. Parameters that result in banded chaos are organized into discrete, nonoverlapping zones in the parameter space. We apply these results to analyze a circle map that models modulated parasystole. Analysis of the model is complicated by the fact that the map has slope less than 1 for part of its domain. However, numerical simulations indicate that the modulated parasystole map displays banded chaos over a wide range of parameters. Banded chaos in this map produces rhythms with a relatively constant sinus-ectopic coupling interval, long trains of uninterrupted sinus beats, and patterns of successive sinus beats between ectopic beats characteristic of those found clinically.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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