Parity Breaking Bifurcation in Inhomogeneous Systems

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Abstract
Parity breaking instabilities of spatially periodic patterns are considered. In homogeneous systems such instabilities produce steadily drifting patterns. Spatial inhomogeneities are shown to lead to pattern pinning. The transition from pinned patterns to drifting ones may be surprisingly complex. Examples are described containing infinite cascades of global bifurcations. The values of the bifurcation parameter at which these occur obey a simple scaling law. The predicted dynamics provide a qualitative understanding of recent experiments on binary fluid convection in an annulus.

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