Quasipatterns in a model for chemical oscillations forced at multiple resonance frequencies

Multifrequency forcing of systems undergoing a Hopf bifurcation to spatially homogeneous oscillations is investigated. For weak forcing composed of frequencies near the 1 1, 1 2, and 1 3 resonances, such systems can be described systematically by a suitably extended complex Ginzburg-Landau equation. Weakly nonlinear analysis shows that, generically, the forcing function can be tuned such that resonant triad interactions with weakly damped modes stabilize subharmonic 4- and 5-mode quasipatterns. In simulations starting from random initial conditions, domains of these quasipatterns compete and yield complex, slowly ordering patterns.