Controlling degenerate Hopf bifurcations

In this paper, a control problem for degenerate Hopf bifurcations is studie d 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 formulat e an appropriate control law for obtaining small-amplitude limit cycles or for modifying the multiplicity of the periodic orbits. Two examples are des cribed for illustration.