Nonlinear analysis in a modified van der Pol oscillator

In this paper we study the nonlinear dynamics of a modified van der Pol oscillator. More precisely, we study the local codimension one, two and three bifurcations which occur in the four parameter family of differential equations that models an extension of the classical van der Pol circuit with cubic nonlinearity. Aiming to contribute to the understand of the complex dynamics of this system we present analytical and numerical studies of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given.