Scale-free networks emerging from multifractal time series

Budroni, M. A., Baronchelli, A. & Pastor-Satorras, R. (2017). Scale-free networks emerging from multifractal time series. Physical Review E (PRE), 95(5), 052311.. doi: 10.1103/PhysRevE.95.052311

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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.

Item Type: Article
Additional Information: Copyright American Physical Society, 2017
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/17545

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