On a Codimension 3 Bifurcation Arising in an Autonomous Electronic Circuit

Some aspects of the bifurcations of a modified van der Pol oscillator are considered. We focus our attention on the bifurcations related to a double-zero degeneracy in the linear part of the equilibrium point in the origin. The analysis of the corresponding normal form shows the possibility of additional degeneracy in the nonlinear part, which leads us to study a 3-parameter family of planar vector fields whose bifurcation set is described.