Yang Lingfa, Dolnik Milos, Zhabotinsky Anatol M, Epstein Irving R
Department of Chemistry and Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
Chaos. 2006 Sep;16(3):037114. doi: 10.1063/1.2214167.
The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing pattern's wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.
最著名的图灵斑图由条纹或斑点的简单六边形排列组成。直到最近，具有其他几何形状的图灵斑图才很少被观察到。在此，我们展示了在一个光敏反应扩散系统中六边形和方形图灵超晶格斑图形成与稳定性的实验研究及数学建模。超晶格由通过一个由简单六边形或方形晶格组成的掩膜照射系统所创建的初始条件发展而来，该掩膜的波长接近固有图灵斑图波长的倍数。我们表明，光化学周期强迫与图灵不稳定性的相互作用产生了强迫模式的多个空间谐波。位于图灵不稳定性带内的谐波在光照关闭后依然存在并形成超晶格。方形超晶格是与时间无关的方形图灵斑图的首个实例。我们还证明，在一个图灵带略低于临界值的系统中，空间均匀的内部或外部振荡能够产生振荡方形斑图。
