摘要
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。
To describe the inner structure of complex systems by multi-fractal theory,the physical significance of the parameters in the multi-fractal spectrum were discussed,and the formula for the calculation of the multi-fractal spectrum were presented.Based on the WTMM method,the signal of the multi-fractal Cantor set,the turbulence and the worm DNA were analyzed.The results show that the information of construction can be inflected by the multi-fractal spectrum and the multi-fractal characteristics of DNA,and the turbulence are similar.The method of WTMM can be used to calculate multi-fractal spectrum of signal in complex system with valid results.
出处
《解放军理工大学学报（自然科学版）》
EI
北大核心
2010年第5期572-577,共6页
Journal of PLA University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(10372038)
