Abstract
Understanding and researching the human body has been fundamental due to its importance for living beings. As one of the vital organs of the human body, the heart has always been of great academic relevance. One of the areas of study of the heart is the study of the electrical stimuli that provide blood pumping. These electrical stimuli come from the Sinoatrial Node (SA), known as the natural pacemaker, which transmits the stimuli to the other parts of the heart, thus allowing blood to be pumped. A model to represent the signals of a pacemaker has been developed using a relaxation oscillator, the Van der Pol oscillator, given by a second-order differential equation. In this particular study, a more comprehensive investigation is proposed by introducing fractional order differential equations. Varying the order of the system allows for a more refined analysis of the dynamic properties of the Van der Pol oscillator and, by extension, of the cardiac pacemaker modeled by it. This approach is especially relevant considering the complex and nonlinear nature of the cardiovascular system. The practical implementation of this model is carried out by means of numerical simulation, using algorithms developed in the Python programming language. This choice of platform allows for efficient and flexible analysis of the resulting signals under different conditions and system parameters. Signal analysis in the time domain is complemented by advanced signal processing techniques in the frequency domain. The Discrete Fourier Transform (DFT) and Continuous Wavelet Transform (CWT) are employed to investigate the system's response at different frequencies, providing an in-depth understanding of its stability and dynamic behavior. In addition, the graphical representation of the results using phase spaces and bifurcation diagrams provides a visual understanding of the complex interactions between the system components and their dependencies on the model parameters.
Published Version
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