Scale-free networks emerging from multifractal time series

Scale-free networks emerging from multifractal time series.

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 th...

Scale-Free Networks Out of Multifractal Chaos

Scale-free networks emerging from weighted random graphs.

We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "supernode network" by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is P(k) approximately k(-lambda) with lambda=2.5. Our results imply that the min...

Fractal and Multifractal Time Series

5 Methods for Non-Stationary Fractal Time-Series Analysis 15 5.1 Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2 Discrete Wavelet Transform (WT) Approach . . . . . . . . . . 16 5.3 Detrended Fluctuation Analysis (DFA) . . . . . . . . . . . . . 16 5.4 Detection of Trends and Crossovers with DFA . . . . . . . . . 19 5.5 Sign and Magnitude (Volatility) DFA . . . . . . . ....

Scale-Free Dynamics Emerging from Information Transfer

– The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is analytically tractable, and show that dynamic criticality is indeed attained. Such emergence of criticality is confirmed numerically in the two-dimensional Ising...