The Van der Pol Equation

In this work, we present the basic theoretical efforts that are known in order to deal with non-trivial solutions of the Van der Pol oscillator, such as theory of average, successive approximations and symbolic dynamics. We also construct a set of diagrams (bifurcation, 2D and 3D Fourier power spectra) and maps, based on numerical investigations, corresponding to the expected theoretical results. Furthermore we examine closely the existence of chaotic attractors, both theoretically (with symbolic dynamics) and numerically (period doubling cascades). We show how we constructed sound files, based on the Fourier spectra, each one corresponding to a periodic, an almost periodic and a chaotic solution, as one of the parameters of the system alters.