Competing parametric instabilities with circular symmetry

John David Crawford*, Edgar Knobloch, Hermann Riecke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Recent experiments in circular geometry have studied the dynamics produced by two parametrically excited surface waves. There is a natural theoretical context for experiments of this type, the mode interaction between two period-doubling bifurcations in the presence of O(2) symmetry. We formulate this interaction as a map in four dimensions, and classify the primary, secondary, and tertiary bifurcations. We find that the observed amplitude oscillations can arise as a tertiary Hopf bifurcation from a mixed mode pattern provided exactly one of the primary instabilities is subcritical.

Original languageEnglish (US)
Pages (from-to)20-24
Number of pages5
JournalPhysics Letters A
Issue number1
StatePublished - Feb 6 1989

ASJC Scopus subject areas

  • General Physics and Astronomy


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