The heart rhythm is one of the most interesting aspects of the dynamic behavior of biological systems. Understanding heart rhythms is essential in the dynamic analysis of the heart. Each type of dynamic behaviour can describe normal or pathological physiology. The heart is made up of nodes ranging from SA node (natural pacemaker) to Purkinje fibers. The electric current originates in the sinus node and travels through the heart until it reaches the Purkinje fibers, causing after its passage through each of the nodes a heartbeat thus constituting the electrocardiogram (ECG). Since the origin of the electric current is the sinus node, in this article we study numerically and experimentally by microcontroller the influence of the sinus node on the propagation of electric current through the heart. A study of the sinus node in its autonomous state shows us that in their coupled state, the nodes of the heart qualitatively reproduce the time series of the action potential of this latter, which leads to the recording of the ECG. A study when the sinus node is subjected to periodic pulsed excitation E 1(t) = kP(t), assumed to come from blood pressure, with P(t) the blood pressure, shows that for some selected frequencies, it is found that the nodes of the heart and the ECG exhibit responses having the same shape and the same frequencies as those of the pulsatile blood pressure. This suggests the possibility of using such a conversion and excitation mechanism to replicate the functioning of cardiac conduction system. The chaotic analysis of the sinus node subjected to a sinusoidal type disturbance (E 0sin(ωt)) is also presented, it shows that in its chaotic state, the nodes of the heart, as well as the ECG, provide very high frequency signals. This requires the control of the sinus node (natural pacemaker) in such a situation

In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term ( ) x sin n is proposed. A generalization in the case of small oscillations on the ( ) x sin n function is studied. Due to ( ) x sin n function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge-Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results. RECEIVED

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The present work studies the dynamical behavior of the Van der Pol oscillator with sine nonlinearity oscillator subjected to the effects of non-sinusoidal excitations through the analysis of bifurcation structures. In this work, a modification of the classical Van der Pol oscillator is carried out by replacing the linear term x with the nonlinear term sinn (x) . The idea is to see the impact of the strength of this function on the appearance of chaotic dynamics for small and large values of the nonlinear dissipation term  . For this purpose, studies by numerical simulation and by analogue simulation are proposed. First, using nonlinear analysis tools, a similarity on the bifurcation sequences is observed despite a difference in the ranks of obtaining the particular behaviours and the bifurcation points. This study is confirmed by their respective maximum Lyapunov exponents. In a second step, a real implementation using microcontroller technology, which is motivated by the use of an artificial pacemaker, is carried out. For a more practical case, the excitation signal is generated by another microcontroller. The study shows a similarity with the results obtained numerically. Thirdly, in order to show that the model can be derived from mathematical modelling, an electronic simulation using OrCAD-Pspice software is also proposed. The results obtained are in qualitative agreement

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