No abstract

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