Numerical Analysis of Heart Rhythm Using Nonlinear Oscillator Coupling

This article presents a mathematical and computational model that emulates the behavior of two muscles of the heart: the sinoatrial node (SA) and atrioventricular node (VA), which is responsible for the cardiac stimulus. The dynamics is described by two coupled Van der Pol oscillators, capable of generating a characteristic wave that resembles the cardiac behavior recorded by the electrocardiogram. Moreover, we proposed the idea of an external force applied to the system, characterized by a non-ideal signal, which comes from the formalism of Bessel functions. This external force is used to analyze the coupling between the nodes and investigate the phase synchronization between the oscillators representing SA and VA. I In order to analyze the nonlinear dynamics presented, we utilized tools such as the Lyapunov exponent, bifurcation diagram, and phase maps. Additionally, another analysis was performed to investigate the phase synchronization behavior between the oscillators. These analyses allow theoretical investigation of cardiac stimuli and some presentations of pathologies such as arrhythmias. These characterization further corroborates future improvements of the mathematical model and assignments of other terms to approximate it more to real ECG examination data.