Subcritical Hopf Equilibrium Points in Boundary of the Stability Region

Authors

  • Josaphat Ricardo Ribeiro Gouveia Jr Federal Institute of Bahia
  • Fabíolo Moraes Amaral Federal Institute of Bahia
  • Luís Fernando Costa Alberto Escola de Engenharia de São Carlos, USP

DOI:

https://doi.org/10.5540/tema.2016.017.02.0211

Keywords:

Dynamical Systems, Nonlinear Systems, Stability Region, Boundary of the Stability Region, Subcritical Hopf equilibrium point.

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.

References

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Published

2016-08-31

How to Cite

Gouveia Jr, J. R. R., Amaral, F. M., & Alberto, L. F. C. (2016). Subcritical Hopf Equilibrium Points in Boundary of the Stability Region. Trends in Computational and Applied Mathematics, 17(2), 211. https://doi.org/10.5540/tema.2016.017.02.0211

Issue

Vol. 17 No. 2 (2016)

Section

Original Article

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