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.
ASJC Scopus subject areas
- Physics and Astronomy(all)