Dynamical behavior analysis of the heart system by the bifurcation structures.

The functioning of the heart rhythm can exhibit a wide variety of dynamic behaviours under certain conditions. In the case of rhythm disorders or cardiac arrhythmias, the natural rhythm of the heart is usually involved in the sinoatrial node, the atrioventricular node, the atria of the carotid sinus, etc. The study of heart related disorders requires an important analysis of its rhythm because the regularity of cardiac activity is conditioned by a large number of factors. The cardiac system is made up of a combination of nodes ranging from the sinus node, the atrioventricular node to its Purkinje bundles, which interact with each other via communicative aspects. Due to the nature of their respective dynamics, the above are treated as self-oscillating elements and modelled by nonlinear oscillators. By modelling the cardiac conduction system as a model of three nonlinear oscillators coupled by delayed connections and subjected to external stimuli depicting the behavior of a pacemaker, its dynamic behavior is studied in this paper by nonlinear analysis tools. From an electrocardiogram (ECG) assessment, the heart rhythm reveals normal and pathological rhythms. Three forms of ventricular fibrillation, ventricular flutter, ventricular tachycardia and atrial fibrillation are observed. The results are confirmed by the respective maximum Lyapunov exponents. Considering the cardiac nodes as microchips, using microcontroller simulation technology, the cardiac conduction system was modelled as a network of four ATmega 328P microcontrollers. A similarity with the results obtained numerically can be observed.

Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients.

This paper, is an analysis of the dynamics of new models of nonlinear systems in which the state damping variables with elastic coefficients, given by functions c cos ⁡ ( p x ) , c sin ⁡ ( p x ) , c cos ⁡ ( p x ˙ ) and c sin ⁡ ( p x ˙ ) are investigated in their autonomous and excited states. They exhibit periodic regions of stability and instability in their autonomous states and a rich dynamic behavior. The analysis of limit cycles shows the presence of isolated curves around the origin (0.0), which explains the presence of periodic solutions (limit cycles). The dynamics obtained allows to describe qualitatively the cardiac activity (artificial pacemaker). A chaos analysis shows the appearance of regular and chaotic behaviors. These studies allowed us to show the effect of the damping of the state variable and the elastic coefficients on the dynamics of these models. The presence of analog functions makes the experimental study complex. An implementation based on microcontroller simulation technology has been proposed. The microcontroller results are consistent with the numerical results.