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.

• Received 28 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.218301