布鲁塞尔子的柱对称破缺的定态结构  

Steady Structures in Column Symmetry Breaking of Brusselator Model

作　　者：刘雪萍[1] 付美荣[1,2] 张进军[1] 

机构地区：[1]山西师范大学化学与材料科学学院,山西临汾041004 [2]长治学院,山西长治046011

出　　处：《山西农业大学学报（自然科学版）》2013年第6期548-552,共5页Journal of Shanxi Agricultural University(Natural Science Edition)

基　　金：山西省软科学项目(2011041015-01);教育部高等学校博士点专项基金(20121404110004);山西省青年科技基金(2011021008-1);山西省人力资源和社会保障部优秀人才专项基金

摘　　要：从布鲁塞尔子的反应扩散方程出发,在柱对称定态解的计算过程的基础上,详细地计算了布鲁塞尔子的柱对称破缺的定态结构解,并绘制了适当参数下柱面及柱内结构的三维浓度分布图。计算及模拟结果表明,若柱对称破缺定态解的第一分支点所对应的控制参数的临界值为Bm′i′n′时,越过该临界值后,柱内结构发生了对称性破缺,原来均匀对称的结构消失,转变为由km′i′和n′共同决定的有序结构。同时还发现,在柱对称破缺条件下,柱内浓度除受r和z影响外,还受到φ的调制,这一结论为我们研究演化着的包括生命体系在内的实际体系中的柱型结构提供了有益的借鉴,为推进耗散结构在实际中的应用打开了一个新局面。In this study, the solution of column symmetry breaking steady structure in Brusselator Model is calculated based on the Brusselator reaction-diffusion equation and the solution of column symmetry steady structures. In addi tion, the 3-D patterns of the surface and inner column symmetric breaking steady structures are also established. The results indicated that when the corresponding critical value of the first branch point is Bm＇i,＇^n＇ , symmetry breaking occurs in the column structure and the new ordered structures are presented when the value is larger than B＇. The new or- dered structures are determined by le,o,i, and n＇ ,and the concentration are not only determined by r and z, hut also modu- lated by 0. These findings provide a helpful guidance for researches on evolution of the column-type structures in living and practical systems, and also promote the application of dissipative structures in practice.

关 键 词：对称性破缺 布鲁塞尔模型 定态结构 

分 类 号：O414.1[理学—理论物理]