Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation

It is a well-known result that in a versal deformation of the Takens-Bogdanov bifurcation is possible to find dynamical systems that undergo saddle-node, homoclinic and Hopf bifurcations. In this document a nonlinear control system in the plane is considered, whose nominal vector field undergoes the Takens-Bogdanov bifurcation, and then the idea is to design a scalar control law such that the closed-loop system undergoes the called controllable Hopf bifurcation.