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.
Conway
Jessica M
JM
Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Riecke
Hermann
H