反应扩散系统中交叉扩散引发的图灵斑图之间的转变  

Cross-diffusion-induced transitions between Turing patterns in reaction-diffusion systems

作　　者：孟星柔 刘若琪 贺亚峰[1] 邓腾坤 刘富成[1] Meng Xing-Rou;Liu Ruo-Qi;He Ya-Feng;Deng Teng-Kun;Liu Fu-Cheng(College of Physics Science and Technology,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

出　　处：《物理学报》2023年第19期267-277,共11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:A2021201003);河北大学自然科学多学科交叉研究计划(批准号:DXK202010)资助的课题。

摘　　要：交叉扩散是影响图灵斑图形成和转变的重要因素之一.本文在反应扩散布鲁塞尔模型中引入交叉扩散项,首先对其进行线性分析和弱非线性分析,然后数值研究了交叉扩散的方向性以及浓度依赖性在图灵斑图转变过程中的作用.在单向交叉扩散情况下,交叉扩散的方向直接决定了斑图转变的次序.阻滞子向活化子的交叉扩散会导致系统逐渐远离初级分岔点,从而引发图灵斑图的正向转变;与之相反,活化子向阻滞子的交叉扩散会导致系统逐渐靠近初级分岔点,从而引发图灵斑图的反向转变.对称双向交叉扩散下,阻滞子向活化子的交叉扩散效应要强于活化子向阻滞子的交叉扩散.交叉扩散系数除了与自身浓度相关外,还与其他物质浓度相关.研究发现浓度依赖交叉扩散也会影响图灵斑图的转变方向.当扩散系数Duv线性依赖阻滞子浓度v变化时,随着浓度线性调节参数β的增大,引发图灵斑图正向转变;相反,当扩散系数Dvu线性依赖活化子浓度u变化时,引发图灵斑图的反向转变.Croo-diffusion io one of the moat important factoro affecting the formation and tranoition of Turing patterne in reaction diffusion oyotems.In thie paper,croo-diffusion io introduced into a reaction diffucion Brusselator model to investigate the effecto of the directivity and denoity-dependence of crose-diffurion on Turing pattern tranoition.Turing apace is obtained by the standard linear atability analyaig,and the amplitude equations are derived baced on weakly nonlinear method,by which Turing pattern selection can be determined theoretically.It is found that the degree of deviation from the primary Turing bifurcation point playe an important role in determining the process of pattern selection in the Turing region.Ao the deviation from onset ia inerenoed,the oyotem exhibite a seriea of pattern tranoitione from homogenoue otate to honeycomb hexagonal pattern,to otripe pattern,and then to hexagonal epot pattern.In the cnse of one-way crooo-diffusion,the direction of croso-diffusion determines the order of Turing pattern tranoition.The croo-diffusion from the inhibitor to the activator enhancea the Turing mode and drivea the cyatem far away from the primary bifurcation point,resulting in the forward order of Turing pattern trancition.On the contrary,the croeo-diffuaion from the activator to the inhibitor ouppreases the Turing mode and forces the pattern tranoition in a reveroe order.In the case of two-way croso-diffusion,the croso-diffusion effect from inhibitors to activators io stronger than that from activatore to inhibitore with the came diffusion coefficient.Easentially,the cros β-diffucion coefficient is dependent on not only the local concentration of apecies itcelf,but also the concentrations of other apecies due to their interaction.It is found that concentration dependent erose diffusion also affecto the tranoformation direction of Turing pattern.When the diffurion cofficient Duv io linearly dependent on the concentration of retardero,the poaitive traneformation of the Turing pattern io induced with the

关 键 词：图灵机理 斑图转变 交叉扩散 方向性 浓度依赖 

分 类 号：O175[理学—数学]