空间周期性驱动对双层耦合反应扩散系统中图灵斑图的影响  

Effects of spatial periodic forcing on Turing patterns in two-layer coupled reaction diffusion system

作　　者：刘倩 田淼 范伟丽[2] 贾萌萌 马凤娜 刘富成[1] Liu Qian;Tian Miao;Fan Wei-Li;Jia Meng-Meng;Ma Feng-Na;Liu Fu-Cheng(College of Physics Science and Technology,Hebei University,Baoding 071002,China;Institute of Environmental Engineering,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学物理科学与技术学院,保定071002 [2]河北大学环境工程研究所,保定071002

出　　处：《物理学报》2022年第9期356-365,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11975089,11875014);河北省自然科学基金(批准号:A2021201010,A2021201003)资助的课题。

摘　　要：周期性驱动是控制斑图最有效的方式之一,因此一直是斑图动力学研究的一大热点.自然界中的斑图形成系统大多是多层耦合的非线性系统,周期性驱动对这些多层耦合系统的作用机理人们还不甚了解.本文通过耦合Brusselator(Bru)系统和Lengyel-Epstein(LE)系统,并给LE系统施加一个空间周期性驱动来研究外部驱动对多层耦合系统中图灵斑图的影响.研究发现,只要外部驱动与Bru系统的超临界图灵模(内部驱动模)两者中的一个为长波模时,就可以将LE系统中的次临界图灵模激发,3个模式共同作用从而形成具有3个空间尺度的复杂斑图.若外部驱动和内部驱动模均为短波模,则无法激发此系统的本征次临界图灵模,但满足空间共振时也可以产生超点阵斑图.若LE系统的本征模为超临界图灵模,其自发形成的六边形斑图只有在外部驱动强度较大的情况下才能够产生响应,且其空间对称性受到外部驱动波数的影响.Periodic forcing of pat tern-forming systems is always a research hot spot in the field of pattern formation since it is one of the most effective methods of controlling patterns.In reality,most of the pattern-forming systems are the multilayered systems,in which each layer is a reaction-diffusion system coupled to adjacent layers.However,few researches on this issue have been conducted in the multilayered systems and their responses to the periodic forcing have not yet been well understood.In this work,the influences of the spatial periodic forcing on the Turing patterns in two linearly coupled layers described by the Brusselator(Bru)model and the Lengyel-Epstein(LE)model respectively have been investigated by introducing a spatial periodic forcing into the LE layer.It is found that the subcritical Turing mode in the LE layer can be excited as long as one of the external spatial forcing and the supercritical Turing mode(referred to as internal forcing mode)of the Bru layer is a longer wave mode.These three modes interact together and give rise to complex patterns with three different spatial scales.If both the spatial forcing mode and the internal forcing mode are the short wave modes,the subcritical Turing mode in the LE layer cannot be excited.But the super lattice pattern can also be generated when the spatial resonance is satisfied.When the eigenmode of the LE layer is supercritical,a simple and robust hexagon pattern with its characteristic wavelength appears and responds to the spatial forcing only when the forcing intensity is large enough.It is found that the wave number of forcing has a powerful influence on the spatial symmetry of patterns.

关 键 词：双层反应扩散系统 空间周期性驱动 图灵斑图 空间共振 

分 类 号：O157.5[理学—数学]