Abstract
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.
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