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.
Scale-free networks emerging from multifractal time series / Budroni, Marcello A.; Baronchelli, Andrea; Pastor-Satorras, Romualdo. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 96:5(2017), p. 052311. [10.1103/PhysRevE.95.052311]
Scale-free networks emerging from multifractal time series
Budroni, Marcello A.
;
2017-01-01
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.