摘要
利用描述可激发介质中波的传播的二维反应扩散方程，首次研究了一类规则分形网络：谢尔宾斯基地毯（SG）上斑图（pattern）的形成．随着控制参量的变化，SG上可以有湍流、螺旋波，以及辫状波等多种形式的斑图；与规则体系比较，分形体系的受限扩散使得复杂斑图的形成受到抑制．在合适的控制参量区内，还发现存在“结构诱导”的脉冲波的周期激发现象以及辫状波向螺旋波、湍流的跃迁．
Up till now, there is no report on the study of self-organisation behavior on fractal networks. However, patten formation on fraeal networks is of great theoretical and experimental importance , for so many things in the world, induding catalyst surface, should be viewed as fractal, and abundant patteerns , e.g., turbulence, spiral waves and soliton waves have been observed in these systems. Using the reactinn diffusion equation which describes wave propagating in excitable media , and adopting the fast simulation method provided by Barkley,the authols studied the pattern formatfon behavior on a kind of determimistic fractal : SierpinskiGasket (SG) with the variation of the control parameters, turbulence, spiral waves andbraid-like waves are observed. One sas that the defects of SG cannot hinder the formation ofregular patterns. Compared to Eudidean space, however, one finds that the fractal structure cansuppress the formation of more complex strctures , i.e., spiral waves or turbulence, which shouldresult from the limtation of diffusion on fractal networks. It's rather interesting that undercertain parameter , a periodic excitation of pulse wave is observed, which collides with thebraid -like wave and then disappeals. One should note that this phenomena is purey 'structure indued'. As a whole, this is the first report of the study on pattem formation in fractal mediaand it is demonstrated that fractal structure can lead to some new features which may calls theattention of scientists .
基金
国家自然科学基金
