Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks

2021 ◽  
Vol 31 (3) ◽  
pp. 033127
Author(s):  
Min Huang ◽  
Zhongkui Sun ◽  
Reik V. Donner ◽  
Jie Zhang ◽  
Shuguang Guan ◽  
...  
Keyword(s):  
Complexity Measures ◽  
Statistical Complexity ◽  
Ordinal Pattern ◽  
Transition Networks

Quantifying the complexity of the delayed logistic map

2011 ◽  
Vol 369 (1935) ◽  
pp. 425-438 ◽  
Author(s):  
Cristina Masoller ◽  
Osvaldo A. Rosso
Keyword(s):  
Probability Distribution Function ◽  
Logistic Map ◽  
Nonlinear Feedback ◽  
Complementary Information ◽  
Complexity Measures ◽  
Pattern Complexity ◽  
Statistical Complexity ◽  
Ordinal Patterns ◽  
Forbidden Patterns ◽  
Ordinal Pattern

Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the ‘histogram-based’ probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of the delay-induced dynamics: there are parameter regions where the histogram-based complexity is zero while the ordinal pattern complexity is not, and vice versa. We also show that the time series generated from the nonlinear delayed logistic map can present zero missing or forbidden patterns, i.e. all possible ordinal patterns are realized into orbits.

scholarly journals Application of Information and Complexity Measures to Neutron Stars Structure

2019 ◽  
Vol 18 ◽  
pp. 163
Author(s):  
K. Ch. Chatzisavvas ◽  
V. P. Psonis ◽  
C. P. Panos ◽  
Ch. C. Moustakidis
Keyword(s):  
Gravitational Field ◽  
Neutron Star ◽  
Neutron Stars ◽  
Short Range ◽  
Nuclear Force ◽  
Low Complexity ◽  
Complexity Measures ◽  
Astronomical Observations ◽  
Equation Of States ◽  
Statistical Complexity

We apply several information and statistical complexity measures to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behaviour are combined and produce a macroscopic dense object. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.

scholarly journals Complexity-like properties and parameter asymptotics of Lq-norms of Laguerre and Gegenbauer polynomials.

2021 ◽  
Author(s):  
Jesus S Dehesa ◽  
Nahual Sobrino
Keyword(s):  
High Energy ◽  
Continuous Variable ◽  
Gegenbauer Polynomials ◽  
Spherically Symmetric ◽  
Complexity Measures ◽  
Physical Systems ◽  
Statistical Complexity ◽  
Momentum Distributions ◽  
Symmetric Quantum ◽  
Parameter Dependent

Abstract The main monotonic statistical complexity-like measures of the Rakhmanov’s probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of them quantifying two configurational facets of spreading, are examined in this work beyond the Cramér-Rao one. The Fisher-Shannon and LMC (López-Ruiz-Mancini-Calvet) complexity measures, which have two entropic components, are analytically expressed in terms of the degree and the orthogonality weight’s parameter(s) of the polynomials. The degree and parameter asymptotics of these two-fold spreading measures are shown for the parameter-dependent families of HOPs of Laguerre and Gegenbauer types. This is done by using the asymptotics of the Rényi and Shannon entropies, which are closely connected to the Lq-norms of these polynomials, when the weight function’s parameter tends towards infinity. The degree and parameter asymptotics of these Laguerre and Gegenbauer algebraic norms control the radial and angular charge and momentum distributions of numerous relevant multidimensional physical systems with a spherically-symmetric quantum-mechanical potential in the high-energy (Rydberg) and high-dimensional (quasi-classical) states, respectively. This is because the corresponding states’ wavefunctions are expressed by means of the Laguerre and Gegenbauer polynomials in both position and momentum spaces.

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