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arXiv · 1612.07070

Scale-free networks emerging from multifractal time series

Marcello A. Budroni·Andrea Baronchelli·Romualdo Pastor-Satorras
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Abstract

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 characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic 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.

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Marcello A. Budroni, Andrea Baronchelli, Romualdo Pastor-Satorras. 2016-12-21. Scale-free networks emerging from multifractal time series. https://doi.org/10.1103/physreve.95.052311

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