Abstract
The dynamics of complex systems, such as ecosystems, financial markets and the human brain, emerge from the interactions of numerous components. We often lack the knowledge to build reliable models for the behaviour of such network systems. This makes it difficult to predict potential instabilities. We show that one could use the natural fluctuations in multivariate time series to reveal network regions with particularly slow dynamics. The multidimensional slowness points to the direction of minimal resilience, in the sense that simultaneous perturbations on this set of nodes will take longest to recover. We compare an autocorrelation-based method with a variance-based method for different time-series lengths, data resolution and different noise regimes. We show that the autocorrelation-based method is less robust for short time series or time series with a low resolution but more robust for varying noise levels. This novel approach may help to identify unstable regions of multivariate systems or to distinguish safe from unsafe perturbations.
Highlights
Many complex systems are managed or structured such that they are relatively stable, in the sense that they can maintain the same functions
In order to find the slowest direction in a multivariate time series, we detect the direction of highest autocorrelation by using the Min/Max autocorrelation factors (MAF) analysis [21], which we explain below
We evaluated the effect of data length and resolution on the performance of MAF and principal component analysis (PCA)
Summary
Many complex systems are managed or structured such that they are relatively stable, in the sense that they can maintain the same functions. Examples include the human body [1], financial systems [2], ecosystems or social systems [3]. It is intuitively straightforward that for each system there is a particular type of perturbation (in the sense that a certain set of network entities is disturbed simultaneously in a particular way) to which the system is the most sensitive [10]. This raises the question of whether we might be able to deduce such ‘weak spots’ in the myriad of possible combinations of pressures on the system
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