湍流与蠕虫的DNA序列的多重分形谱分析

为了用多重分形谱理论定量描述复杂系统的内部结构,详细讨论了多重分形谱中各参量的物理意义,给出了计算多重分形谱的公式,并采用小波WTMM(wavelet transform maxima modulus)算法计算了多分形Cantor集、湍流和DNA序列的多重分形谱。研究结果表明:多分形谱分析能够得到序列(或集合)不均匀的整体分布信息,湍流与DNA的多分形特性十分相似,DNA比湍流更不均匀,"混乱"特性似乎更充分,基于小波算法的WTMM理论可以用来计算复杂现象的多分形谱,计算结果是可信的。

Multi-fractal spectrum for signal time series of turbulence and worm DNA

To describe the inner st ructure of complex systems by mult i-fr actal theor y, the phy sical significance of the parameters in the mult i-fractal spectr um were discussed, and the formula for the calculatio n of the mult i-fractal spect rum w ere presented. Based o n the WT MM method, the signal of the mul ti-f ractal Cantor set , the turbulence and the wo rm DNA w ere analy zed. T he result s show that the informatio n of co nstr uct io n can be inflected by the mult i-fractal spectrum and the mult i-f ractal char acterist ics o f DNA, and the turbulence are similar. The method of WTMM can be used to calculate mult i-fr actal spectrum of sig nal in complex system with v al id result s