Rescaled Range Permutation Entropy: A Method for Quantifying the Dynamical Complexity of Extreme Volatility in Chaotic Time Series

Abstract

Information entropy, as a quantitative measure of complexity in nonlinear systems, has been widely researched in a variety of contexts. With the development of a nonlinear dynamic, the entropy is faced with severe challenges in dealing with those signals exhibiting extreme volatility. In order to address this problem of weighted permutation entropy, which may result in the inaccurate estimation of extreme volatility, we propose a rescaled range permutation entropy, which selects the ratio of range and standard deviation as the weight of different fragments in the time series, thereby effectively extracting the maximum volatility. By analyzing typical nonlinear systems, we investigate the sensitivities of four methods in chaotic time series where extreme volatility occurs. Compared with sample entropy, fuzzy entropy, and weighted permutation entropy, this rescaled range permutation entropy leads to a significant discernibility, which provides a new method for distinguishing the complexity of nonlinear systems with extreme volatility.

Determination of neutron-skin thickness using configurational information entropy

“…Many applications of CIE methods can be found in Korteweg-de Vries (KdV) solitions, compact astrophysical systems, and scalar glueballs (see a brief introduction in Ref. [23]), theoretical research of new Higgs boson decay channels [30], deploying heavier eta meson states in AdS/QCD [31], confinement/deconfinement transition in QCD [32], quarkonium in a finite density plasma [33], time evolution in physical systems [34,35], etc. In projectile fragmentation reactions, fragment distributions show a sensitive dependence on the change in neutron density [36][37][38], which makes it possible to determine the neutron skin thickness of neutron-rich nuclei.…”

Cascade discrete memristive maps for enhancing chaos*

“…Chaotic and hyperchaotic behaviors can be found in continuous and discrete nonlinear dynamical systems, [10][11][12][13][14][15][16][17] which have many unique behaviors, including topological transitivity, initial state sensitivity, and periodic orbit density. [18][19][20][21] In order to obtain new chaotic systems with rich repertoires of nonlinear behaviors, memristors were introduced into some classical chaotic circuits. [22][23][24][25] In addition, a cascade method of forming a series of new systems by cascading two chaotic subsystems was proposed in our previous papers.…”