Conway Jessica M, Riecke Hermann
Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev Lett. 2007 Nov 23;99(21):218301. doi: 10.1103/PhysRevLett.99.218301. Epub 2007 Nov 21.
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.
研究了经历霍普夫分岔至空间均匀振荡的系统的多频强迫。对于由接近1:1、1:2和1:3共振频率组成的弱强迫，此类系统可通过适当扩展的复金兹堡-朗道方程进行系统描述。弱非线性分析表明，一般而言，可调节强迫函数，使得与弱阻尼模式的共振三重态相互作用稳定亚谐波4模式和5模式准模式。在从随机初始条件开始的模拟中，这些准模式的区域相互竞争并产生复杂的、缓慢有序的模式。
