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Symmetry
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Symmetry in Nonlinear Studies
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Symmetry in Nonlinear Studies

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

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 14473

Special Issue Editor

Prof. Dr. Manuel De La Sen

E-Mail Website
Guest Editor
Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, Leioa (Bizkaia), Spain
Interests: automation control systems; applied mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The properties of symmetry are very relevant in certain problems of theoretical physics and mathematics, as well as in many applications, for instance, related to Noether-type theorems, Lie symmetry, conservation laws, or studies of biological and medical problems modelled based on patchy environments. These problems are important for the theoretical development of “ad-hoc” models of differential-difference equations or those based on graph theory. However, there are also real problems where the symmetry is either lost or not taken formally into account to derive the expected relevant properties—for instance, those related to asymmetric patchy environments in epidemic models or the formal use of frameworks of quasimetrics rather than metrics in fixed-point theory and some of its applications. This Special Issue of the journal Symmetry invites contributions illustrating the bridges between mathematical and real-life scientific or applied problems and the relevance to them of symmetry- and/or asymmetry-related physical or modelling constraints. A tentative list of topics of interest for the Issue follows below, but it is also open for other related topics.

Prof. Dr. Manuel De La Sen
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. 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

  • Symmetry, asymmetry and Noether theorems
  • Lie and Noether symmetries
  • Conservation laws related to symmetry and asymmetry properties
  • Graph theory and symmetry
  • New results on graph theory related to symmetry and asymmetry properties
  • Symmetries and asymmetries in patchy environments for epidemic models
  • Symmetries and asymmetries in biological and medical models
  • Symmetries and asymmetries in optimization problems
  • Symmetries and asymmetries in nonlinear time-delay, discrete-time dynamics, and control systems
  • New results on the relevance of symmetry and asymmetry in fixed-point theory and related areas
  • Applications of fixed-point theory linked to symmetry and asymmetry properties
  • Symmetry and asymmetry problems in nonlinear functional equations
  • Conservation laws and symmetry
  • Symmetry and asymmetry in nonlinear studies
  • Symmetries of differential equations
  • Symmetries and asymmetries in fractional calculus
  • Other related topics.

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Published Papers (6 papers)

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Research

21 pages, 870 KiB  
Article
An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters
by Usa Humphries, Grienggrai Rajchakit, Ramalingam Sriraman, Pramet Kaewmesri, Pharunyou Chanthorn, Chee Peng Lim and Rajendran Samidurai
Symmetry 2020, 12(6), 1035; https://doi.org/10.3390/sym12061035 - 20 Jun 2020
Cited by 21 | Viewed by 2486
Abstract
The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical [...] Read more.
The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
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17 pages, 2123 KiB  
Article
Symmetry-Breaking for Airflow Control Optimization of an Oscillating-Water-Column System
by Fares M’zoughi, Izaskun Garrido and Aitor J. Garrido
Symmetry 2020, 12(6), 895; https://doi.org/10.3390/sym12060895 - 1 Jun 2020
Cited by 6 | Viewed by 2184
Abstract
Global optimization problems are mostly solved using search methods. Therefore, decreasing the search space can increase the efficiency of their solving. A widely exploited technique to reduce the search space is symmetry-breaking, which helps impose constraints on breaking existing symmetries. The present article [...] Read more.
Global optimization problems are mostly solved using search methods. Therefore, decreasing the search space can increase the efficiency of their solving. A widely exploited technique to reduce the search space is symmetry-breaking, which helps impose constraints on breaking existing symmetries. The present article deals with the airflow control optimization problem in an oscillating-water-column using the Particle Swarm Optimization (PSO). In an effort to ameliorate the efficiency of the PSO search, a symmetry-breaking technique has been implemented. The results of optimization showed that shrinking the search space helped to reduce the search time and ameliorate the efficiency of the PSO algorithm. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
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13 pages, 301 KiB  
Article
On (ψ, ϕ)-Rational Contractions
by Andreea Fulga
Symmetry 2020, 12(5), 723; https://doi.org/10.3390/sym12050723 - 3 May 2020
Cited by 5 | Viewed by 1744
Abstract
In this paper, we examine the notion of ( ψ , ϕ )-contractions by involving rational forms in the context of complete metric spaces. We note that some well-known fixed point theorems for rational forms can be deduced from our main results. We [...] Read more.
In this paper, we examine the notion of ( ψ , ϕ )-contractions by involving rational forms in the context of complete metric spaces. We note that some well-known fixed point theorems for rational forms can be deduced from our main results. We also consider some examples to indicate the validity of the presented results. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
19 pages, 451 KiB  
Article
A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks
by Pharunyou Chanthorn, Grienggrai Rajchakit, Usa Humphries, Pramet Kaewmesri, Ramalingam Sriraman and Chee Peng Lim
Symmetry 2020, 12(5), 683; https://doi.org/10.3390/sym12050683 - 25 Apr 2020
Cited by 44 | Viewed by 2723
Abstract
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a [...] Read more.
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
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15 pages, 5730 KiB  
Article
Real-Time Control for the EHU Stellarator
by Izaskun Garrido, Javier Maseda, Itziar Martija and Aitor J. Garrido
Symmetry 2020, 12(1), 11; https://doi.org/10.3390/sym12010011 - 19 Dec 2019
Viewed by 1958
Abstract
At present, two main magnetic confinement fusion devices exist: tokamaks and stellarators. Moreover, stellarators have been demonstrated to be a good alternative to tokamaks, due to their ability to operate in continuous mode, which eventually translates into a higher commercial profitability. In stellarators, [...] Read more.
At present, two main magnetic confinement fusion devices exist: tokamaks and stellarators. Moreover, stellarators have been demonstrated to be a good alternative to tokamaks, due to their ability to operate in continuous mode, which eventually translates into a higher commercial profitability. In stellarators, the magnetic confinement of the plasma is achieved exclusively by the coils, thus no electric current through the plasma is needed. In particular, this article presents the Columbia Non-Neutral Torus stellarator that is located in the Automatic Control Group of Euskal Herriko Unibertsitatea (EHU). This EHU stellarator maintains symmetry in its structure due to the topology of the mesh that is formed by its coils. A cornerstone of future fusion reactors is to obtain real-time control that enables a sustained reaction. In this article, a control-oriented model for the installed magnetic confinement coils is presented. The model is based on matrices that preserve symmetry, which is defined from physical principles and then validated by different sets of experimental data. Then, based on this model, a novel predictive control suited to this particular model with symmetric objective function is implemented in the numerical simulations, and its response is compared to that of traditional controllers. Finally, this control is implemented in a real plant and the satisfactory experiment results provide validation of both the numerical model and proposed controller. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
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10 pages, 256 KiB  
Article
Some New Observations and Results for Convex Contractions of Istratescu’s Type
by Z. D. Mitrović, H. Aydi, N. Mlaiki, M. Gardašević-Filipović, K. Kukić, S. Radenović and M. de la Sen
Symmetry 2019, 11(12), 1457; https://doi.org/10.3390/sym11121457 - 27 Nov 2019
Cited by 11 | Viewed by 2852
Abstract
The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and [...] Read more.
The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
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