Open AccessSubcritical Hopf Equilibrium Points in Boundary of the Stability Region
Author(s) -
Josaphat R. R. Gouveia,
Fabíolo Moraes Amaral,
Luís Alberto
Publication year - 2016
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2016.017.02.0211
Subject(s) - transversality , boundary (topology) , mathematics , stability (learning theory) , characterization (materials science) , equilibrium point , hopf bifurcation , mathematical analysis , class (philosophy) , boundary value problem , stable manifold , nonlinear system , physics , bifurcation , differential equation , computer science , quantum mechanics , machine learning , artificial intelligence , optics
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.