The mechanism of formation and transformation of white-eye square patterns in dielectric barrier discharge system is investigated numerically, using the two-layer Lengyel–Epstein model with asymmetric and symmetric coupling. When the scale of the simulation system [Formula: see text] is two to three times of pattern wavelength [Formula: see text], it is found that an obvious intermediate state with square distribution appears by adjusting the ratio of diffusion coefficients [Formula: see text]/[Formula: see text]. When it is coupled with a suitable short-wavelength Turing mode in the range of [Formula: see text] to [Formula: see text], a new spatial resonance structure can be formed in the short-wavelength mode subsystem, and the pattern evolves from a simple square pattern to a white-eye square pattern. Although the two coupling methods achieve the same results, the duration time of the white-eye square pattern in the symmetric coupling method is significantly longer than that in the asymmetric coupling method. Because the quadratic coefficient of the amplitude equation in the reaction–diffusion system is not zero, the simple square pattern of the long wavelength mode subsystem gradually transits into a stable hexagon pattern gradually. As a result, the white-eye pattern transits from a square to a hexagon.

中文翻译：

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介质阻挡放电系统中白眼方形超晶格图案形成与转变的数值分析

使用具有不对称和对称耦合的两层 Lengyel-Epstein 模型，对介质阻挡放电系统中白眼方形图案的形成和转变机制进行了数值研究。当模拟系统的规模【公式：见正文】为图案波长的2～3倍【公式：见正文】时，通过调整扩散系数的比值发现出现明显的呈方形分布的中间态【公式：见正文]/[公式：见正文]。当它与[公式：见正文]到[公式：见正文]范围内的合适的短波长图灵模式耦合时，可以在短波长模式子系统中形成新的空间共振结构，并且图案演变从简单的方形图案到白眼方形图案。虽然两种耦合方法达到了相同的结果，但对称耦合方法中白眼正方形图案的持续时间明显长于非对称耦合方法。由于反应-扩散系统中振幅方程的二次系数不为零，长波长模式子系统的简单方形图案逐渐转变为稳定的六边形图案。结果，白眼图案从正方形转变为六边形。长波长模式子系统的简单方形图案逐渐转变为稳定的六边形图案。结果，白眼图案从正方形转变为六边形。长波长模式子系统的简单方形图案逐渐转变为稳定的六边形图案。结果，白眼图案从正方形转变为六边形。