Special Issue "Entropy, Nonlinear Dynamics and Complexity"

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

Deadline for manuscript submissions: 30 November 2019.

Special Issue Editor

Prof. Dr. Lucas Lacasa
E-Mail Website
Guest Editor
School of Mathematical Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK
Interests: complex systems; time series analysis; network science; nonlinear dynamics; statistical physics

Special Issue Information

Dear Colleagues,

Concepts such as ‘entropy’ or ‘complexity’ have been approached from many different angles in physics, mathematics, computer science and beyond. The interdisciplinary arena spanned by these concepts inherits ideas and tools from nonlinear dynamics (e.g. Kolmogorov–Sinai entropy, Renyi entropies), information theory (Shannon entropy, statistical complexity), statistical physics (Boltzmann entropy, Tsallis entropy), or network science (graph entropy), and make use of these to describe and understand the behaviour of complex systems in an amazingly wide range of contexts.

The aim of this Special Issue is to encourage researchers to present original and recent developments on topics closely related to entropy and complexity that emerge (typically) in nonlinear dynamical systems and related complex systems. The type of contributions can be theoretical or applied: they can address a particular fundamental open problem where the authors push forward the state of the art or can represent sensible examples that make efficient use of these tools in different contexts across physics, biology, economics or the computational social sciences, among others.

I look forward to reading your submissions.

Prof. Dr. Lucas Lacasa
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 papers will be 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 1600 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
  • Complexity measures
  • Complex systems
  • Networks
  • Time series analysis
  • Disordered systems
  • Nonlinear dynamical systems

Published Papers (5 papers)

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Research

Open AccessArticle
Multiscale Entropy Analysis of Postural Stability for Estimating Fall Risk via Domain Knowledge of Timed-Up-And-Go Accelerometer Data for Elderly People Living in a Community
Entropy 2019, 21(11), 1076; https://doi.org/10.3390/e21111076 - 02 Nov 2019
Abstract
As people in developed countries live longer, assessing the fall risk becomes more important. A major contributor to the risk of elderly people falling is postural instability. This study aimed to use the multiscale entropy (MSE) analysis to evaluate postural stability during a [...] Read more.
As people in developed countries live longer, assessing the fall risk becomes more important. A major contributor to the risk of elderly people falling is postural instability. This study aimed to use the multiscale entropy (MSE) analysis to evaluate postural stability during a timed-up-and-go (TUG) test. This test was deemed a promising method for evaluating fall risk among the elderly in a community. The MSE analysis of postural instability can identify the elderly prone to falling, whereupon early medical rehabilitation can prevent falls. Herein, an objective approach is developed for assessing the postural stability of 85 community-dwelling elderly people (aged 76.12 ± 6.99 years) using the short-form Berg balance scale. Signals were collected from the TUG test using a triaxial accelerometer. A segment-based TUG (sTUG) test was designed, which can be obtained according to domain knowledge, including “Sit-to-Walk (STW),” “Walk,” “Turning,” and “Walk-to-Sit (WTS)” segments. Employing the complexity index (CI) of sTUG can reveal information about the physiological dynamics’ signal for postural stability assessment. Logistic regression was used to assess the fall risk based on significant features of CI related to sTUG. MSE curves for subjects at risk of falling (n = 19) exhibited different trends from those not at risk of falling (n = 66). Additionally, the CI values were lower for subjects at risk of falling than those not at risk of falling. Results show that the area under the curve for predicting fall risk among the elderly subjects with complexity index features from the overall TUG test is 0.797, which improves to 0.853 with the sTUG test. For the elderly living in a community, early assessment of the CI for sTUG using MSE can help predict the fall risk. Full article
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
Open AccessArticle
Multiscale Horizontal Visibility Graph Analysis of Higher-Order Moments for Estimating Statistical Dependency
Entropy 2019, 21(10), 1008; https://doi.org/10.3390/e21101008 - 16 Oct 2019
Abstract
The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based [...] Read more.
The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based on the horizontal visibility graph. We describe how a horizontal visibility graph may be calculated based on second-order and third-order statistical moments. We compare the new methods with the first-order measure, and then give examples including stock markets and aero-engine performance parameters. These analyses suggest that measures derived from the horizontal visibility graph may be of particular relevance to the growing interest in quantifying the information exchange between time series. Full article
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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Open AccessArticle
A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics
Entropy 2019, 21(10), 955; https://doi.org/10.3390/e21100955 - 29 Sep 2019
Abstract
It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical [...] Read more.
It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments. Full article
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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Open AccessArticle
Remaining Useful Life Prediction with Similarity Fusion of Multi-Parameter and Multi-Sample Based on the Vibration Signals of Diesel Generator Gearbox
Entropy 2019, 21(9), 861; https://doi.org/10.3390/e21090861 - 03 Sep 2019
Abstract
The prediction of electrical machines’ Remaining Useful Life (RUL) can facilitate making electrical machine maintenance policies, which is important for improving their security and extending their life span. This paper proposes an RUL prediction model with similarity fusion of multi-parameter and [...] Read more.
The prediction of electrical machines’ Remaining Useful Life (RUL) can facilitate making electrical machine maintenance policies, which is important for improving their security and extending their life span. This paper proposes an RUL prediction model with similarity fusion of multi-parameter and multi-sample. Firstly, based on the time domain and frequency domain extraction of vibration signals, the performance damage indicator system of a gearbox is established to select the optimal damage indicators for RUL prediction. Low-pass filtering based on approximate entropy variance (Aev) is introduced in this process because of its stability. Secondly, this paper constructs Dynamic Time Warping Distance (DTWD) as a similarity measurement function, which belongs to the nonlinear dynamic programming algorithm. It performed better than the traditional Euclidean distance. Thirdly, based on DTWD, similarity fusion of multi-parameter and multi-sample methods is proposed here to achieve RUL prediction. Next, the performance evaluation indicator Q is adopted to evaluate the RUL prediction accuracy of different methods. Finally, the proposed method is verified by experiments, and the Multivariable Support Vector Machine (MSVM) and Principal Component Analysis (PCA) are introduced for comparative studies. The results show that the Mean Absolute Percentage Error (MAPE) of the similarity fusion of multi-parameter and multi-sample methods proposed here is below 14%, which is lower than MSVM’s and PCA’s. Additionally, the RUL prediction based on the DTWD function in multi-sample similarity fusion exhibits the best accuracy. Full article
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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Open AccessArticle
Recurrence Networks in Natural Languages
Entropy 2019, 21(5), 517; https://doi.org/10.3390/e21050517 - 23 May 2019
Abstract
We present a study of natural language using the recurrence network method. In our approach, the repetition of patterns of characters is evaluated without considering the word structure in written texts from different natural languages. Our dataset comprises 85 ebookseBooks written in 17 [...] Read more.
We present a study of natural language using the recurrence network method. In our approach, the repetition of patterns of characters is evaluated without considering the word structure in written texts from different natural languages. Our dataset comprises 85 ebookseBooks written in 17 different European languages. The similarity between patterns of length m is determined by the Hamming distance and a value r is considered to define a matching between two patterns, i.e., a repetition is defined if the Hamming distance is equal or less than the given threshold value r. In this way, we calculate the adjacency matrix, where a connection between two nodes exists when a matching occurs. Next, the recurrence network is constructed for the texts and some representative network metrics are calculated. Our results show that average values of network density, clustering, and assortativity are larger than their corresponding shuffled versions, while for metrics like such as closeness, both original and random sequences exhibit similar values. Moreover, our calculations show similar average values for density among languages which that belong to the same linguistic family. In addition, the application of a linear discriminant analysis leads to well-separated clusters of family languages based on based on the network-density properties. Finally, we discuss our results in the context of the general characteristics of written texts. Full article
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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