Controlling degenerate Hopf bifurcations

In this paper, a control problem for degenerate Hopf bifurcations is studied by means of modifying the amplitude and multiplicity of limit cycles via feedback from a graphical approach performed in the frequency domain. This approach uses diverse elements from the familiar Hopf bifurcation mechanism, degenerate Hopf bifurcation theory, and Poincare normal forms to formulate an appropriate control law for obtaining small-amplitude limit cycles or for modifying the multiplicity of the periodic orbits. Two examples are described for illustration.