Hopf bifurcation and the Hopf fibration

M. Field, J. W. Swift

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We present techniques for studying the local dynamics generated by an equivariant Hopf bifurcation. We show that under general hypotheses we can expect the formation of a branch of attracting invariant spheres which capture all the local dynamics. In addition, using the Hopf fibration, we show that the limit cycles generated by the Hopf bifurcation are determined by zeros of a vector field defined on complex projective space. We show how to compute these zeros and illustrate our methods with examples of Hopf bifurcations for the dihedral groups of order six and eight and the orthogonal groups.

Original languageEnglish (US)
Article number005
Pages (from-to)385-402
Number of pages18
Issue number2
StatePublished - 1994

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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