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Disordered Systems, Fractals and Chaos

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 16982

Special Issue Editor

1. School of Business,University of Leicester, Brookfield, Leicester LE2 1RQ, UK
2.Department of Statistics and Econometrics, Bucharest University of Economic Studies, 010374 Bucharest, Romania
Interests: econophysics; sociophysics; nonlinear dynamics; nonequilibrium systems; networks; phase transitions; growth (and decay) models; fractals; scientometrics; statistical physics; materials sciences and applied mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is difficult to know what came first, and which one developed faster, nowadays, with the complex levels that have been reached by the study of disordered systems, fractals, and chaos. Disordered systems likely pre-date the techniques allowing their properties to be described in terms of fractals (and scaling arguments) and, in particular, their chaotic features. The level of complexity is such that in disordered systems, it is hard to disentangle the concepts from the analysis of features.

This allows the two aspects to intermingle without losing their separate identities. In fact, one should not separate, unmix, or disjoin, such features.

Fractal phenomena in disordered systems are, nowadays, of such general knowledge that a Special Issue based on “entropy” is particularly appealing, since one can cover a broad range of both “old” and “new” topics. These include the geometric formulation of aggregates and rough interfaces, as the first applications, in addition to studies of fractal networks and from the very current studies of (multilayered or otherwise) networks up to the study of nonequilibrium processes (generalized classical entropy concepts), multifractals, random multiplicative processes, earthquakes, and, even now, economic, sociological, and medical applications. Indeed, the discovery of “stylized facts” in financial data was concomitant to fractional Brownian motion developments, whence gathering the three items for this issue: disordered systems, fractals, and chaos. I do not discount any test based on scaling ideas, like Benford law. Nowadays, there are also challenges in the medical field, not only EEG, but also taking a much larger perspective on biomedical engineering, neuroscience, and (networked or otherwise) physiology. I would even re-include botany, more generally “ecology”, with regard to population dynamics. A rather relevant field pertaining to the Special Issue theme is “opinion dynamics”—text analyses should also be of renewed interest. Accounting tests can also lead to enthusiastic papers connecting fractals and chaos in a new “natural” way.

As long as we are aware that entropy is a measure of diversity, we should connect with all disordered systems; we should look at power laws, and discuss their validity limit, without any fear; and we should prepare nonlinear (dynamic) equations for obtaining “order from chaos”. We know that part of the challenge stems from “real things”, in measuring properties, thereafter modeling, and, if possible, forecasting. We should be open minded. We are.

Thus, it is proposed that the articles comprising this Special Issue should provide our colleagues with a good sense of the remarkable diversity and important applications of fractals, with theoretical and practical features in any type of disordered system. A huge variety of perspectives can be presented. We wish to be one for all, and all for one. One paper on our beloved investigation topic will serve many. There are no limits.

Prof. Dr. Marcel Ausloos
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entropy
  • fractals
  • chaos
  • networks
  • econophysics
  • sociophysics
  • ecology
  • opinion dynamics
  • aggregates
  • physiology
  • applied linguistics
  • power laws
  • systemic risk
  • nonequilibrium states
  • multifractals
  • fractional Brownian motion
  • time series

Published Papers (5 papers)

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Research

23 pages, 6427 KiB  
Article
Entropic Analysis of Votes Expressed in Italian Elections between 1948 and 2018
by Stefano Marmani, Valerio Ficcadenti, Parmjit Kaur and Gurjeet Dhesi
Entropy 2020, 22(5), 523; https://doi.org/10.3390/e22050523 - 04 May 2020
Cited by 5 | Viewed by 3314
Abstract
In Italy, the elections occur often, indeed almost every year the citizens are involved in a democratic choice for deciding leaders of different administrative entities. Sometimes the citizens are called to vote for filling more than one office in more than one administrative [...] Read more.
In Italy, the elections occur often, indeed almost every year the citizens are involved in a democratic choice for deciding leaders of different administrative entities. Sometimes the citizens are called to vote for filling more than one office in more than one administrative body. This phenomenon has occurred 35 times after 1948; it creates the peculiar condition of having the same sample of people expressing decisions on political bases at the same time. Therefore, the Italian contemporaneous ballots constitute the occasion to measure coherence and chaos in the way of expressing political opinion. In this paper, we address all the Italian elections that occurred between 1948 and 2018. We collect the number of votes per party at each administrative level and we treat each election as a manifestation of a complex system. Then, we use the Shannon entropy and the Gini Index to study the degree of disorder manifested during different types of elections at the municipality level. A particular focus is devoted to the contemporaneous elections. Such cases implicate different disorder dynamics in the contemporaneous ballots, when different administrative level are involved. Furthermore, some features that characterize different entropic regimes have emerged. Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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12 pages, 484 KiB  
Article
Analysis of Social Media Impact on Opportunity Recognition. A Social Networks and Entrepreneurial Alertness Mixed Approach
by Sebastian Ion Ceptureanu, Eduard Gabriel Ceptureanu, Marian Pompiliu Cristescu and Gurjeet Dhesi
Entropy 2020, 22(3), 343; https://doi.org/10.3390/e22030343 - 17 Mar 2020
Cited by 14 | Viewed by 4578
Abstract
This paper investigates the effects of social media on entrepreneurial opportunity recognition. Combining the internal and external approaches of opportunity recognition, the study analyzes how social media influences the entrepreneurs in discovering new entrepreneurial opportunities. Structural equation modeling was used in this study, [...] Read more.
This paper investigates the effects of social media on entrepreneurial opportunity recognition. Combining the internal and external approaches of opportunity recognition, the study analyzes how social media influences the entrepreneurs in discovering new entrepreneurial opportunities. Structural equation modeling was used in this study, using the variance-based partial least squares (PLS)–structural equation modeling (SEM), on a sample of 354 entrepreneurs. We concluded that social media directly and positively influences entrepreneurial opportunity recognition while entrepreneurial alertness (internal approach) and social networks (external approach) partially mediates its indirect effects on entrepreneurial opportunity recognition. The study contributes to the existing literature by bringing new insights into the entrepreneurial opportunity recognition process by focusing on a poorly represented factor in the literature, social media. Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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19 pages, 2988 KiB  
Article
An Intrinsic Entropy Model for Exchange-Traded Securities
by Claudiu Vințe, Ion Smeureanu, Titus-Felix Furtună and Marcel Ausloos
Entropy 2019, 21(12), 1173; https://doi.org/10.3390/e21121173 - 29 Nov 2019
Cited by 6 | Viewed by 3201
Abstract
This paper introduces an intrinsic entropy model which can be employed as an indicator for gauging investors’ interest in a given exchange-traded security, along with the state of the overall market corroborated by individual security trading data. Although the syntagma of intrinsic entropy [...] Read more.
This paper introduces an intrinsic entropy model which can be employed as an indicator for gauging investors’ interest in a given exchange-traded security, along with the state of the overall market corroborated by individual security trading data. Although the syntagma of intrinsic entropy might sound somehow pleonastic, since entropy itself characterizes the fundamentals of a system, we would like to make a clear distinction between entropy models based on the values that a random variable may take, and the model that we propose, which employs actual stock exchange trading data. The model that we propose for the intrinsic entropy does not include any exogenous factor that could influence the level of entropy. The intrinsic entropy signals if the market is either inclined to buy the security or rather to sell it. We further explore the usage of the intrinsic entropy model for algorithmic trading, in order to demonstrate the value of our model in assisting investors’ intraday stock portfolio selection, along with timely generated signals for supporting the buy/sell decision-making process. The test results provide empirical evidence that the proposed intrinsic entropy model can be used as an indicator for evaluating the direction and the intensity of intraday trading activity of an exchange-traded security. The data employed for testing consisted of historical intraday transactions executed on The Bucharest Stock Exchange (BVB). Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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13 pages, 1177 KiB  
Article
Ordered Avalanches on the Bethe Lattice
by Malgorzata J. Krawczyk, Paweł Oświęcimka, Krzysztof Kułakowski and Stanisław Drożdż
Entropy 2019, 21(10), 968; https://doi.org/10.3390/e21100968 - 03 Oct 2019
Cited by 3 | Viewed by 2452
Abstract
We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b [...] Read more.
We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to s τ . When the avalanche mass is conserved ( k = b ), we get τ = 1 . For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent τ is found to depend on the model parameters; τ     l o g ( b ) / l o g ( k ) . The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength α m a x in the bifractal spectrum is found to be 1 / τ . Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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13 pages, 8871 KiB  
Article
Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy
by Chunyuan Liu, Lina Ding and Qun Ding
Entropy 2019, 21(7), 663; https://doi.org/10.3390/e21070663 - 06 Jul 2019
Cited by 10 | Viewed by 2805
Abstract
The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, [...] Read more.
The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, a multi-scale entropy theory analysis and statistical analysis are carried out on the chaotic sequences produced by different parameters and different initial values of logistic systems. According to the simulation results, the complexity of the chaotic system represented by the logistic system is mainly decided by parameter μ. Not all characteristic parameters of the chaotic system depend on the initial values. It is possible to make a reasonable estimation and prediction of the chaotic system from a macroscopic level. A variance estimation method for the parameter μ is proposed and applied to a logistic system and to another chaotic system, which is equally effective. Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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