Complex Patterns in Resonantly Forced Chemical Oscillations

Herman Riecke, Northwestern U,

A multitude of quasi-patterns and superlattice patterns have been observed in vertically vibrated fluid layers (Faraday waves). We show that the mechanisms underlying the formation of these patterns with multiple length scales can be exploited to excite such patterns also in a different class of systems: systems exhibiting a Hopf bifurcation to spatially homogeneous oscillations. A classic example is the oscillatory Belousov-Zhabotinsky reaction. Our weakly nonlinear analysis and direct numerical simulation of the relevant complex Ginzburg-Landau equation incorporating multi-resonant forcing reveal stable quasi-patterns with four- and five-fold rotational symmetries and their competition.