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

Authors

  • F.M. Amaral
  • L. F. C. Alberto
  • N. G. Bretas

DOI:

https://doi.org/10.5540/tema.2010.011.02.0111

Abstract

Abstract. Under the assumption that all equilibrium points are hyperbolic, the stability boundary of nonlinear autonomous dynamical systems is characterized as the union of the stable manifolds of equilibrium points on the stability boundary. The existing characterization of the stability boundary is extended in this paper to consider the existence of non-hyperbolic equilibrium points on the stability boundary. In particular, a complete characterization of the stability boundary is presented when the system possesses a type-zero saddle-node equilibrium point on the stability boundary. It is shown that the stability boundary consists of the stable manifolds of all hyperbolic equilibrium points on the stability boundary and of the stable manifold of the type-zero saddle-node equilibrium point.

References

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Published

2010-06-01

How to Cite

Amaral, F., Alberto, L. F. C., & Bretas, N. G. (2010). Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of a type-zero saddle-node equilibrium point. Trends in Computational and Applied Mathematics, 11(2), 111–120. https://doi.org/10.5540/tema.2010.011.02.0111

Issue

Vol. 11 No. 2 (2010)

Section

Original Article

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