Local numerical analysis of Hopf bifurcation

Vladimír Janovský, Petr Plecháč

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6 Citations (Scopus)

Abstract

This paper contributes to a local numerical analysis of Hopf bifurcation in the sense of a bordered systems approach. However, the method proposed enables us to decide about stability exchange between a stable steady-state and bifurcating orbit without explicit knowledge about the spectrum of the monodromy matrix. A kind of numerical Liapunov-Schmidt reduction is presented as a tool for continuation and Newton-like corrector of Hopf points. The proposed algorithm gives necessary data for local qualitative analysis of the Hopf bifurcation. The data enable us to determine degeneracy of the Hopf bifurcation and stability of bifurcating orbits and to predict periodic orbits. The equivariant form of the reduction and its application are discussed as well.

Original languageEnglish
Pages (from-to)1150-1168
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume33
Issue number3
Publication statusPublished - Jun 1996

Keywords

  • Bordered matrices
  • Equivariant bifurcation
  • Hopf bifurcation
  • Liapunov-Schmidt reduction
  • Stability exchange

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    Janovský, V., & Plecháč, P. (1996). Local numerical analysis of Hopf bifurcation. SIAM Journal on Numerical Analysis, 33(3), 1150-1168.