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Complex and Fractional Dynamical Systems

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

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 27392

Special Issue Editors

Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal
Interests: complex systems modelling; automation and robotics; fractional order systems modelling and control; data analysis and visualization
Special Issues, Collections and Topics in MDPI journals
Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto, 4249-015 Porto, Portugal
Interests: nonlinear dynamics; fractional calculus; modeling; control; evolutionary computing; genomics; robotics, complex systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex systems (CS) are composed of a large number of autonomous but non-independent interacting components. CS are ubiquitous in many areas of natural and social sciences, engineering, and mathematics. Their behavior is often characterized by long-range correlations in the time–space domain, memory effects, fractality, and power law dynamics. These properties have been well described using the tools of fractional calculus that generalize classical calculus to non-integer orders. On the other hand, in recent years, big data were applied in the scope of complex systems to find solutions for the challenges and problems facing their study. It was verified that data analysis, organization, retrieval, and modeling are relevant tools for a computational approach to tackle complex and fractional systems.

The Special Issue focuses on original and new research results on complex system dynamics in science and engineering. Manuscripts on complexity, nonlinearity, fractional dynamics, big data problems, and information theory are solicited. We welcome submissions addressing novel issues as well as those on more specific topics illustrating the broad impact of entropy-based techniques in complexity, nonlinearity, and fractionality.

Papers should fit the scope of the journal Entropy, and topics of interest include (but are not limited to):

  • Complex dynamics;
  • Nonlinear dynamical systems;
  • Big data;
  • Advanced control systems;
  • Fractional calculus and its applications;
  • Evolutionary computing;
  • Finance and economy dynamics;
  • Fractals and chaos;
  • Biological systems and bioinformatics;
  • Nonlinear waves and acoustics;
  • Image and signal processing;
  • Transportation systems;
  • Geosciences;
  • Astronomy and cosmology.

Prof. Dr. António M. Lopes
Prof. José A. Tenreiro Machado
Guest Editors

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

  • dynamics
  • complex systems
  • fractional calculus
  • entropy
  • information
  • big data

Published Papers (4 papers)

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Research

20 pages, 1659 KiB  
Article
Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems
by Nadjette Debbouche, Shaher Momani, Adel Ouannas, ’Mohd Taib’ Shatnawi, Giuseppe Grassi, Zohir Dibi and Iqbal M. Batiha
Entropy 2021, 23(3), 261; https://0-doi-org.brum.beds.ac.uk/10.3390/e23030261 - 24 Feb 2021
Cited by 11 | Viewed by 1949
Abstract
This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the [...] Read more.
This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamical Systems)
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19 pages, 5883 KiB  
Article
A Comparative Study of Two Fractional-Order Equivalent Electrical Circuits for Modeling the Electrical Impedance of Dental Tissues
by Norbert Herencsar, Todd J. Freeborn, Aslihan Kartci and Oguzhan Cicekoglu
Entropy 2020, 22(10), 1117; https://0-doi-org.brum.beds.ac.uk/10.3390/e22101117 - 03 Oct 2020
Cited by 11 | Viewed by 2521
Abstract
Background: Electrical impedance spectroscopy (EIS) is a fast, non-invasive, and safe approach for electrical impedance measurement of biomedical tissues. Applied to dental research, EIS has been used to detect tooth cracks and caries with higher accuracy than visual or radiographic methods. Recent studies [...] Read more.
Background: Electrical impedance spectroscopy (EIS) is a fast, non-invasive, and safe approach for electrical impedance measurement of biomedical tissues. Applied to dental research, EIS has been used to detect tooth cracks and caries with higher accuracy than visual or radiographic methods. Recent studies have reported age-related differences in human dental tissue impedance and utilized fractional-order equivalent circuit model parameters to represent these measurements. Objective: We aimed to highlight that fractional-order equivalent circuit models with different topologies (but same number of components) can equally well model the electrical impedance of dental tissues. Additionally, this work presents an equivalent circuit network that can be realized using Electronic Industries Alliance (EIA) standard compliant RC component values to emulate the electrical impedance characteristics of dental tissues. Results: To validate the results, the goodness of fits of electrical impedance models were evaluated visually and statistically in terms of relative error, mean absolute error (MAE), root mean squared error (RMSE), coefficient of determination (R2), Nash–Sutcliffe’s efficiency (NSE), Willmott’s index of agreement (WIA), or Legates’s coefficient of efficiency (LCE). The fit accuracy of proposed recurrent electrical impedance models for data representative of different age groups teeth dentin supports that both models can represent the same impedance data near perfectly. Significance: With the continued exploration of fractional-order equivalent circuit models to represent biological tissue data, it is important to investigate which models and model parameters are most closely associated with clinically relevant markers and physiological structures of the tissues/materials being measured and not just “fit” with experimental data. This exploration highlights that two different fractional-order models can fit experimental dental tissue data equally well, which should be considered during studies aimed at investigating different topologies to represent biological tissue impedance and their interpretation. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamical Systems)
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15 pages, 2663 KiB  
Article
Classification of Covid-19 Coronavirus, Pneumonia and Healthy Lungs in CT Scans Using Q-Deformed Entropy and Deep Learning Features
by Ali M. Hasan, Mohammed M. AL-Jawad, Hamid A. Jalab, Hadil Shaiba, Rabha W. Ibrahim and Ala’a R. AL-Shamasneh
Entropy 2020, 22(5), 517; https://0-doi-org.brum.beds.ac.uk/10.3390/e22050517 - 01 May 2020
Cited by 111 | Viewed by 19588
Abstract
Many health systems over the world have collapsed due to limited capacity and a dramatic increase of suspected COVID-19 cases. What has emerged is the need for finding an efficient, quick and accurate method to mitigate the overloading of radiologists’ efforts to diagnose [...] Read more.
Many health systems over the world have collapsed due to limited capacity and a dramatic increase of suspected COVID-19 cases. What has emerged is the need for finding an efficient, quick and accurate method to mitigate the overloading of radiologists’ efforts to diagnose the suspected cases. This study presents the combination of deep learning of extracted features with the Q-deformed entropy handcrafted features for discriminating between COVID-19 coronavirus, pneumonia and healthy computed tomography (CT) lung scans. In this study, pre-processing is used to reduce the effect of intensity variations between CT slices. Then histogram thresholding is used to isolate the background of the CT lung scan. Each CT lung scan undergoes a feature extraction which involves deep learning and a Q-deformed entropy algorithm. The obtained features are classified using a long short-term memory (LSTM) neural network classifier. Subsequently, combining all extracted features significantly improves the performance of the LSTM network to precisely discriminate between COVID-19, pneumonia and healthy cases. The maximum achieved accuracy for classifying the collected dataset comprising 321 patients is 99.68%. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamical Systems)
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13 pages, 6844 KiB  
Article
Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform
by Marcin Bąkała, Piotr Duch, J. A. Tenreiro Machado, Piotr Ostalczyk and Dominik Sankowski
Entropy 2020, 22(3), 300; https://0-doi-org.brum.beds.ac.uk/10.3390/e22030300 - 05 Mar 2020
Cited by 3 | Viewed by 2394
Abstract
This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used [...] Read more.
This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamical Systems)
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