Supercritical Hopf equilibrium points on the boundary of the stability region

A complete characterization of the boundary of the stability region of nonlinear autonomous dynamical systems is developed admitting the existence of a particular type of non-hyperbolic equilibrium point on the stability boundary, the supercritical Hopf equilibrium points. Under condition of transversality, it is shown that the stability boundary is comprised of all stable manifolds of the hyperbolic equilibrium points lying on the stability boundary union with the center-stable andor center manifolds of the type-k, k ≥ 1, supercritical Hopf equilibrium points on the stability boundary.