Direct Hopf Bifurcation in Parametric Resonance of Hybridized Waves

Details Direct Hopf Bifurcation in Parametric Resonance of Hybridized Waves Direct Hopf Bifurcation in Parametric Resonance of Hybridized Waves

1996-06-04

arxiv.org/abs/patt-sol/9605006v1

Phys. Rev. Lett., 77 (1996) 179

Nonlinear Sciences

Pattern Formation and Solitons

Appears in Phys. Rev. Lett., RevTeX file and three postscript figures. Packaged using the 'uufiles' utility, 33 kB

Scientific paper

10.1103/PhysRevLett.77.179

We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation leading to quasiperiodic traveling waves. It occurs, for example, if the group velocities of both waves have different signs and the damping is weak. The dynamics above the threshold is briefly discussed. Examples concerning ferromagnetic spin waves and surface waves of ferro fluids are discussed.

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