双层耦合Lengel-Epstein模型中的超点阵斑图

摘要

The influence of Turing modes in two subsystems on pattern formation is investigated by using the two-layer coupled Lengel-Epstein model.It is found that the wave number ratio between two Turing modes play an important role in the pattern formation and pattern selection.When the wave number ratio is 1,no coupling behavior occurs between two subsystems and only stripe and hexagon patterns arise in system.If the wave number ratio lies in a range of 1—17,a variety of superlattice patterns,such as dark-dot,bar-dot and complex super hexagons,I-type or II-type white-eye,honeycomb-like,and superhexagon of circle,are obtained due to the resonance interaction between the two Turing modes in the coupled systems.When the wave number ratio is greater than 17,the superhexagon of circle is always selected and unchanged.Some superlattice patterns above,including stripes,hexagons,super hexagon,Ⅱ-type white-eye,and honeycomb-like patterns,are observed experimentally in a dielectric barrier discharge （DBD） system.In addition,the curves for variation of hexagon pattern wave number with the increase of the product of two diffusion coefficients are obtained and it is found that the wave number becomes smaller with DuDv increasing.%用双层耦合的Lengel-Epstein模型,研究了两个子系统的图灵模对斑图的影响,发现其波数比在斑图的形成和选择过程中起着重要作用.当波数比为1时,双层系统未能发生耦合,只能出现条纹和六边形斑图;当波数比处于1—17的范围时,两子系统发生耦合,图灵模之间发生共振相互作用,得到种类丰富的超点阵斑图,包括暗点、点-棒和复杂超六边、Ⅰ-型和Ⅱ-型白眼、类蜂窝和环状超六边等斑图;当波数比大于17,系统选择的斑图类型不再变化,均为环状超六边斑图.数值模拟得到的条纹、六边形、超六边点阵、Ⅱ-型白眼斑图和类蜂窝斑图均已在介质阻挡放电系统实验中观察到.另外,还得到了超点阵斑图的波数随两个扩散系数乘积DuDv的变化曲线,发现其随的DuDv增大而减小.