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The aim of this paper was to propose a formal approach of the Windowed Detrended Cross-Correlation (WDCC) analysis, a method designed for identifying the processes that underlie intra- and interpersonal synchronization. We present the three main theoretical frameworks that have been proposed for accounting for synchronization processes, (1) the information-processing approach, (2) the coupled oscillators model and (3) the complexity matching effect. We formally derive the WDCC results that could be expected from each model. We show by simulation that each model allows generating series that fit the expected results. We also analyze experimental data sets collected in situations that were supposed to selectively elicit the synchronization processes depicted in the three theoretical frameworks. Our results show that the information-processing and the complexity matching processes are both present in each situation, but with a clear dominance of one of these processes on the other. Finally our results lead us to cast some doubts about the relevance of the coupled oscillators model in interpersonal synchronization.

Detrended Fluctuation Analysis is a widely used method, which aims at assessing the level of self-similarity in time series. This method analyzes the diffusion properties of the signal, by computing the linear regression slope in the diffusion plot, representing in log–log coordinates the relationship between the variability of the signal and the length of the intervals over which this variability is computed. We compare in this paper the results obtained with logarithmically spaced and evenly spaced diffusion plots. The study shows the substantial benefits of evenly spacing, especially in the reduction of the variability of estimation.

International audience; The complexity matching effect supposes that synchronization between complex systems could emerge from multiple interactions across multiple scales and has been hypothesized to underlie a number of daily-life situations. Complexity matching suggests that coupled systems tend to share similar scaling properties, and this phenomenon is revealed by a statistical matching between the scaling exponents that characterize the respective behaviors of both systems. However, some recent papers suggested that this statistical matching could originate from local adjustments or corrections, rather than from a genuine complexity matching between systems. In the present paper, we propose an analysis method based on correlation between multifractal spectra, considering different ranges of time scales. We analyze several datasets collected in various situations (bimanual coordination, interpersonal coordination, and walking in synchrony with a fractal metronome). Our results show that this method is able to distinguish between situations underlain by genuine statistical matching and situations where statistical matching results from local adjustments.