A Minimal Model Dynamics for Twelvefold Quasipatterns

Gomila, Damià; Walgraef, Daniel
Physical Review E 89, 032923 (2014)

A dynamical model of the Swift-Hohenberg type is proposed to describe the formation of twelvefold
quasipatterns as observed, for instance, in optical systems. The model incorporates the general
mechanisms leading to quasipattern formation and does not need external forcing to generate them.
Besides quadratic nonlinearities, the model takes into account an angular dependence of the nonlinear
couplings between spatial modes with different orientations. Furthermore the marginal stability
curve presents other local minima than the one corresponding to critical modes, as usual in optical
systems. Quasipatterns form when one of these secondary minima may be associated with harmonics
built on pairs of critical modes. The model is analyzed numerically and in the framework of
amplitude equations. The results confirm the importance of harmonics to stabilize quasipatterns
and assess the applicability of the model to other systems with similar generic properties.

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