A complex system contains generally many elements that are networked by their couplings. The time series of output records of the system’s dynamical process is subsequently a cooperative result of the couplings. Discovering the coupling structure stored in the time series is an essential task in time series analysis. However, in the currently used methods for time series analysis the structural information is merged completely by the procedure of statistical average. We propose a concept called mode network to preserve the structural information. Firstly, a time series is decomposed into intrinsic mode functions and residue by means of the empirical mode decomposition solution. The mode functions are employed to represent the contributions from different elements of the system. Each mode function is regarded as a mono-variate time series. All the mode functions form a multivariate time series. Secondly, the co-occurrences between all the mode functions are then used to construct a threshold network (mode network) to display the coupling structure. This method is illustrated by investigating gait time series. It is found that a walk trial can be separated into three stages. In the beginning stage, the residue component dominates the series, which is replaced by the mode function numbered M 14 with peaks covering ∼680 strides (∼12 min) in the second stage. In the final stage more and more mode functions join into the backbone. The changes of coupling structure are mainly induced by the co-occurrent strengths of the mode functions numbered as M 11, M 12, M 13, and M 14, with peaks covering 200–700 strides. Hence, the mode network can display the rich and dynamical patterns of the coupling structure. This approach can be extended to investigate other complex systems such as the oil price and the stock market price series.

The scale-invariance behavior has been widely observed in English or other phonetic language texts. In the present study, we examine whether the semantic language, Chinese can also show this behavior. Typically, the scale-invariance behavior is examined in the series of character intervals for the four great Chinese novels by a method of detrended fluctuation analysis. We observe that the scale-invariance behavior characterized by a scaling exponent around 0.60 exists in each novel. Moreover, we divide each novel into three parts with equal number of chapters, and we also observe the existence of scale-invariance in the interval series for each part. Interestingly, we find that there is evident difference in the scaling exponents between the first (or second) part and the third part in the novel of A dream of red mansions, and the difference between parts is not evident for the other three novels. Our observation suggests that there are two writing styles in A dream of red mansions, which are consistent with current prevailing view that the first 80 chapters and the last 40 chapters were accomplished by Xueqin Cao and E Gao, respectively. Our method may shed light on the identification of writing styles in written texts.