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Scale-free networks emerging from multifractal time series

par Budroni, Marcello ;Baronchelli, Andrea;Pastor-Satorras, Romualdo
Référence Physical Review E, 96, 5, 052311
Publication Publié, 2017

Article révisé par les pairs

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Résumé :

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology and validate our findings with extensive numerical simulations. We finally present a numerical analysis on the properties of weighted and directed network projections.