Subcritical Hopf Equilibrium Points in Boundary of the Stability Region

Abstract

ABSTRACT.A complete characterization of the boundary of the stability region of a class of nonlinear autonomous dynamical systems is developed admitting the existence of Subcritical Hopf nonhyperbolic equilibrium points on the boundary of the stability region. The characterization of the stability region developed in this paper is an extension of the characterization already developed in the literature, which considers only hyperbolic equilibrium point. Under the transversality condition, it is shown the boundary of the stability region is comprised of the stable manifolds of all equilibrium points on the boundary of the stability region, including the stable manifolds of the subcritical Hopf equilibrium points of type k, with 0 ≤ k ≤ n − 2, which belong to the boundary of the stability region.