The heart has a leading and vital role in the human body, scientific researches dealing with this theme are sources of growing interest. In recent years, several mathematical models of the heart electrical conduction system have appeared in the scientific literature. In the present paper, the nonlinear dynamics of a heart’s electrical conduction system model is investigated. The model consists of three coupled nonlinear oscillators with time delay coupling as earlier proposed by Gois et al[1]. Our study here is both theoretical and experimental; theoretical study includes fixed points analysis, bifurcations analysis where the effect of some parameters on the system dynamics is investigated, coexisting bifurcations and hysteresis phenomenon are found for some range of the system parameters, Lyapunov exponents and basin of attraction calculation. The experimental study includes sizing an analog implementation of the mathematical model using OrCAD/Pspice software, as well as the practical realisation of the model. Experimental and practical results are then presented in order to confirm theoretical predictions.Keywords: Heart, Electrical Cardiac conduction system, Electrocardiogram, Modified Van der Pol oscillators, Bifurcation, Chaos, OrCAD/Pspice Simulations.

The aim of this work is to investigate the nonlinear dynamics of a forced cardiac pacemaker model represented by a forced modified van der Pol oscillator by using the method of harmonic balance and the method of multiple time scales. The amplitudes of the forced harmonic, primary resonant state, super-harmonic and sub-harmonic resonant state oscillations are obtained and the effects of some system parameters on these amplitudes are investigated; hysteresis and jump phenomena are found. Three similar oscillators are then coupled together via time-delay coupling to model the heart rhythm and the effect of the coupling factor and time delay is also investigated. The overall model is then discretized using the fourth-order Runge–Kutta algorithm. A corresponding very high-speed integrated circuit hardware description language code is then written, synthesised and implemented using the Vivado-2017.4 software for the Artix7-xc7a35tftg256-1 field programmable gate array chip. The chip statistics, time series electrocardiograms and phase portraits of the model are derived; a good correlation between theoretical results (obtained with MATLAB program and Vivado software) and practical results is observed.