An improvement on measure methods of the complexity theory and its applications

A new method is proposed to transform the time series gained from adynamic system to a symbolic series which extracts both overalland local information of the time series. Based on thetransformation, two measures are defined to characterize thecomplexity of the symbolic series. The measures reflect thesensitive dependence of chaotic systems on initial conditions andthe randomness of a time series, and thus can distinguish periodicor completely random series from chaotic time series even though thelengths of the time series are not long. Finally, the logistic mapand the two-parameter Henón map are studied and the results aresatisfactory.