Abstract
On a versal deformation of the Bautin bifurcation it is possible to find dynamical systems that undergo Hopf or non-hyperbolic limit cycle bifurcations. Our paper concerns a nonlinear control system in the plane whose nominal vector field has a pair of purely imaginary eigenvalues. We find conditions to control the Hopf and Bautin bifurcation using the symmetric multilinear vector functions that appear in the Taylor expansion of the vector field around the equilibrium. The control law designed by us depends on two bifurcation parameters and four control parameters, which establish the stability of the equilibrium point and the orientation and stability of the limit cycles. Two examples are given.
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