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Symmetry
Special Issues
Nonlinear Symmetric Systems and Chaotic Systems in Engineering
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Nonlinear Symmetric Systems and Chaotic Systems in Engineering

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 13503

Special Issue Editors

Prof. Dr. Marek Berezowski

E-Mail Website
Guest Editor
Faculty of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 30-155 Kraków, Poland
Interests: analysis and modeling of nonlinear dynamic systems; chemical reactors
Dr. Marcin Lawnik

E-Mail Website
Guest Editor
Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Interests: chaos; cryptography
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many physical, chemical, and even economic phenomena are modeled using nonlinear dynamics. Despite the great interest in the subject shown by scientists and engineers, much remains to be done in these areas. Nonlinear systems characterized by chaotic dynamics are of particular interest to the scientific community. Their analysis will allow us to understand and eliminate many undesirable and dangerous phenomena. On the other hand, chaotic systems are used in many engineering fields, and their use allows for the improvement or even construction of appropriate engineering systems.

This Special Issue focuses on the modelling of nonlinear symmetric processes, their analysis, and application areas. Authors of original papers on mathematical modelling of nonlinear processes using ordinary differential equations (ODEs) and partial differential equations (PDEs), methods of solving such models, and their analysis are invited to submit their papers. In addition, articles focusing on symmetry in nonlinear analysis, methods and numerical analysis, control theory, stability theory, and applications of nonlinear models in various engineering areas are also very welcome.

Prof. Dr. Marek Berezowski
Dr. Marcin Lawnik
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. Symmetry 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 2400 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

  • nonlinear dynamics
  • chaotic dynamics
  • nonlinear methods
  • mathematical modelling
  • control theory
  • applications of chaos and nonlinear dynamics

Published Papers (4 papers)

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Research

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12 pages, 800 KiB  
Article
On Perturbative Methods for Analyzing Third-Order Forced Van-der Pol Oscillators
by Weaam Alhejaili, Alvaro H. Salas, Elsayed Tag-Eldin and Samir A. El-Tantawy
Symmetry 2023, 15(1), 89; https://doi.org/10.3390/sym15010089 - 29 Dec 2022
Cited by 5 | Viewed by 1108
Abstract
In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and the multiple scales method. Both the first- and second-order approximations for the unforced and forced jerk Van-der Pol oscillatory equations are derived [...] Read more.
In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and the multiple scales method. Both the first- and second-order approximations for the unforced and forced jerk Van-der Pol oscillatory equations are derived in detail using the proposed methods. Comparative analysis is performed between the analytical approximations using the proposed methods and the numerical approximations using the fourth-order Runge–Kutta scheme. Additionally, the global maximum error to the analytical approximations compared to the Runge–Kutta numerical approximation is estimated. Full article
(This article belongs to the Special Issue Nonlinear Symmetric Systems and Chaotic Systems in Engineering)
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14 pages, 1626 KiB  
Article
Image Encryption Based on Local Fractional Derivative Complex Logistic Map
by Hayder Natiq, Nadia M. G. Al-Saidi, Suzan J. Obaiys, Mohammed Najah Mahdi and Alaa Kadhim Farhan
Symmetry 2022, 14(9), 1874; https://doi.org/10.3390/sym14091874 - 08 Sep 2022
Cited by 7 | Viewed by 1373
Abstract
Local fractional calculus (fractal calculus) plays a crucial role in applications, especially in computer sciences and engineering. One of these applications appears in the theory of chaos. Therefore, this paper studies the dynamics of a fractal complex logistic map and then employs this [...] Read more.
Local fractional calculus (fractal calculus) plays a crucial role in applications, especially in computer sciences and engineering. One of these applications appears in the theory of chaos. Therefore, this paper studies the dynamics of a fractal complex logistic map and then employs this map to generate chaotic sequences for a new symmetric image encryption algorithm. Firstly, we derive the fractional complex logistic map and investigate its dynamics by determining its equilibria, geometric properties, and chaotic behavior. Secondly, the fractional chaotic sequences of the proposed map are employed to scramble and alter image pixels to increase resistance to decryption attacks. The output findings indicate that the proposed algorithm based on fractional complex logistic maps could effectively encrypt various kinds of images. Furthermore, it has better security performance than several existing algorithms. Full article
(This article belongs to the Special Issue Nonlinear Symmetric Systems and Chaotic Systems in Engineering)
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18 pages, 11092 KiB  
Article
New Chaotic System: M-Map and Its Application in Chaos-Based Cryptography
by Marcin Lawnik and Marek Berezowski
Symmetry 2022, 14(5), 895; https://doi.org/10.3390/sym14050895 - 27 Apr 2022
Cited by 15 | Viewed by 2462
Abstract
One of the applications of dynamical systems with chaotic behavior is data encryption. Chaos-based cryptography uses chaotic dynamical systems as the basis for creating algorithms. The present article discusses a new dynamical system called M-map with its analysis: fixed points, bifurcation diagram, Lyapunov [...] Read more.
One of the applications of dynamical systems with chaotic behavior is data encryption. Chaos-based cryptography uses chaotic dynamical systems as the basis for creating algorithms. The present article discusses a new dynamical system called M-map with its analysis: fixed points, bifurcation diagram, Lyapunov exponent, and invariant density. The obtained bifurcation diagram and the plot of the Lyapunov exponent (with a minimum value of ln2 and a maximum value of ln4) suggest that the so-called robust chaos characterizes this map. Moreover, the obtained results are compared with other dynamical systems used in cryptography. Additionally, the article proposes a new image encryption algorithm. It uses, among others, cyclically shifted S-box or saving encrypted pixels on the first or last free space in the cipher-image. The conducted analysis shows that the cipher-images are characterized by an entropy value close to 8, a correlation of adjacent pixels value close to 0, or values of Number of Pixel of Change Rate (NPCR) and Unified Average Changing Intensity (UACI) measures close to 100% and 33%, respectively. Full article
(This article belongs to the Special Issue Nonlinear Symmetric Systems and Chaotic Systems in Engineering)
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Review

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43 pages, 2125 KiB  
Review
Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
by Bhukya Ramadevi and Kishore Bingi
Symmetry 2022, 14(5), 955; https://doi.org/10.3390/sym14050955 - 07 May 2022
Cited by 20 | Viewed by 7332
Abstract
Traditional statistical, physical, and correlation models for chaotic time series prediction have problems, such as low forecasting accuracy, computational time, and difficulty determining the neural network’s topologies. Over a decade, various researchers have been working with these issues; however, it remains a challenge. [...] Read more.
Traditional statistical, physical, and correlation models for chaotic time series prediction have problems, such as low forecasting accuracy, computational time, and difficulty determining the neural network’s topologies. Over a decade, various researchers have been working with these issues; however, it remains a challenge. Therefore, this review paper presents a comprehensive review of significant research conducted on various approaches for chaotic time series forecasting, using machine learning techniques such as convolutional neural network (CNN), wavelet neural network (WNN), fuzzy neural network (FNN), and long short-term memory (LSTM) in the nonlinear systems aforementioned above. The paper also aims to provide issues of individual forecasting approaches for better understanding and up-to-date knowledge for chaotic time series forecasting. The comprehensive review table summarizes the works closely associated with the mentioned issues. It includes published year, research country, forecasting approach, application, forecasting parameters, performance measures, and collected data area in this sector. Future improvements and current studies in this field are broadly examined. In addition, possible future scopes and limitations are closely discussed. Full article
(This article belongs to the Special Issue Nonlinear Symmetric Systems and Chaotic Systems in Engineering)
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