STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT-Reference-Cited by-同舟云学术

STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT

Published:2013-12 Issue:12 Volume:23 Page:1350196
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

GOUVEIA JOSAPHAT R. R.¹,AMARAL FABÍOLO MORAES¹,ALBERTO LUÍS F. C.²

Affiliation:

1. Mathematics of Collegiate, College Eunápolis – Federal Institute of Bahia, 458222-000, Eunápolis, BA, Brazil

2. University of São Paulo, School of Engineering of São Carlos, Department of Electrical Engineering, 13.566-590 São Carlos, São Paulo, Brazil

Abstract

A complete characterization of the boundary of the stability region (or area of attraction) of nonlinear autonomous dynamical systems is developed admitting the existence of a particular type of nonhyperbolic equilibrium point on the stability boundary, the supercritical Hopf equilibrium point. Under a 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 and\or center manifolds of the type-k, k ≥ 1, supercritical Hopf equilibrium points on the stability boundary.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127413501964

Reference22 articles.

1. Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of a type-zero saddle-node equilibrium point

2. Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

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