Hopf bifurcation by frustrated drifts

Abstract

We describe, with a Hopf bifurcation induced by frustrated drifts, a phenomenon in pattern formation. This generic effect occurs in systems with broken continuous translational and reflection symmetry. Above the bifurcation point periodic or aperiodic motion occurs depending on the actual manifestation of the symmetry breaking. The qualitative aspects of the phenomenon are discussed within a generalized Swift-Hohenberg equation. In addition, based on detailed calculations, also a geometry for a Rayleigh-B\'enard experiment is proposed, where the effect can be investigated experimentally.