Controllability near a Hopf bifurcation

The authors study controllability properties of control affine systems depending on a parameter and with constrained control values. If the uncontrolled system is subject to a Hopf bifurcation, a continuum of periodic solutions bifurcates from an equilibrium. This, together with an accessibility condition, induces for a small control range a two-parameter bifurcation of the control sets (i.e., the regions of complete controllability) around the equilibria and the periodic solutions, respectively. The proofs are based on methods from dynamical systems theory applied to the associated control flow