异质环境下各向异性扩散对图灵斑图的影响  

Effects of anisotropic diffusion on Turing patterns in heterogeneous environment

作　　者：刘若琪 贾萌萌 范伟丽[2] 贺亚峰[1] 刘富成[1] Liu Ruo-Qi;Jia Meng-Meng;Fan Wei-Li;He Ya-Feng;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24期420-426,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12275064,11975089,11875014);河北省自然科学基金(批准号:A2021201010,A2021201003);河北大学自然科学多学科交叉研究计划(批准号:DXK202010,DXK202108)资助的课题.

摘　　要：扩散在图灵斑图形成和演化过程中起到了至为关键的作用.本文采用双变量反应扩散模型,数值研究了异质环境下各向异性扩散对图灵斑图的影响.模拟结果表明:各向异性扩散程度较大时,系统斑图呈条纹斑图,其空间取向由偏离分岔点程度大的扩散系数所决定;各向异性扩散程度较小时,斑图与各向同性扩散情况相同.当扩散系数在空间中线性增长时,由于空间异质性的影响,不同区域可以选择不同的斑图类型,斑图之间存在竞争.当扩散系数受到一维周期性函数调控时,斑图类型和波长由调控函数的波长以及系统本征波长所决定.当调制波长大于本征波长时,系统可呈现不同类型交替的双尺度混合斑图.此外,还发现非对角扩散系数D不仅影响了斑图的选择机制,还扩展了图灵空间的参数范围.Diffusion plays a crucial role in the forming and evolving of Turing patterns.Generally,the diffusion processes in complex systems do not comply to the complete random walk theory,which means that the diffusion is abnormal rather than normal,such as super-diffusion,sub-diffusion and anisotropic diffusion.However,most of previous studies focused on the pattern formation mechanism under the normal diffusion.In this paper,a two-component reaction-diffusion model with anisotropic diffusion is used to study the effect of anisotropic diffusion on Turing patterns in heterogeneous environments.Three different types of anisotropic diffusions are utilized.It is shown that the system gives rise to stripe patterns when the degree of anisotropic diffusion is high.The directions of stripes are determined by the degree of the diffusion coefficient deviating from the bifurcation point.In a low degree of anisotropic diffusion,the pattern type is the same as the counterpart in a low degree of the isotropic diffusion.When the diffusion coefficient grows linearly in the space,different types of patterns compete with each other and survive in different regions under the influence of spatial heterogeneity.When the diffusion coefficient is modulated by a one-dimensional periodic function,both type and wavelength of the pattern are determined by the modulated wavelength and the intrinsic wavelength.The system can exhibit alternating two-scale mixed patterns of different types when the modulated wavelength is larger than the intrinsic wavelength.Note that each of the diffusion coefficients of some special anisotropic media is a tensor,which can be expressed as a matrix in two-dimensional cases.We also study the influence of off-diagonal diffusion coefficient D on Turing pattern.It is found that the Turing pattern induced by off-diagonal diffusion coefficient always selects the oblique stripe pattern.The off-diagonal diffusion coefficient D not only affects the pattern selection mechanism,but also expands the parameter range of Turing spa

关 键 词：反应扩散系统 图灵斑图 各向异性扩散 空间异质性 

分 类 号：O157.5[理学—数学]