On the nonlinear dynamics of a cardiac electrical conduction system model: theoretical and experimental study

Abstract

Abstract 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 [S R F S M Gois and M A Savi, 2009 ‘An analysis of heart rhythm dynamics using a three-coupled oscillator model,’ Chaos, Solitons Fractals, 41, 2553-2565]. 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.