Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023

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

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 8493

Special Issue Editors

School of Information Science and Engineering, Hunan Women’s University, Changsha 410002, China
Interests: differential inclusions; neural networks; mathematical biology and stability analysis of dynamic systems
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China
Interests: the stability of discontinuous systems and applications to the neural networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry is pleased to introduce a Special Issue on the theories and applications related to symmetry/asymmetry. The aim of this Special Issue is to highlight papers that address the dynamics, control, optimization, and applications of nonlinear systems. This has recently become an increasingly popular subject, with an impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers that share this objective are especially welcome. 

Prof. Dr. Quanxin Zhu
Dr. Zuowei Cai
Dr. Fanchao Kong
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

  • symmetry/asymmetry phenomena
  • symmetry dynamics
  • symmetry and differential equations
  • stability and stabilization
  • synchronization
  • symmetry optimization

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (8 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

16 pages, 289 KiB  
Article
Generalized Forward–Backward Methods and Splitting Operators for a Sum of Maximal Monotone Operators
by Hongying Xiao, Zhaofeng Li, Yuanyuan Zhang and Xiaoyou Liu
Symmetry 2024, 16(7), 880; https://doi.org/10.3390/sym16070880 - 11 Jul 2024
Viewed by 822
Abstract
Suppose each of A1,,An is a maximal monotone, and βB is firmly nonexpansive with β>0. In this paper, we have two purposes: the first is finding the zeros of [...] Read more.
Suppose each of A1,,An is a maximal monotone, and βB is firmly nonexpansive with β>0. In this paper, we have two purposes: the first is finding the zeros of j=1nAj+B, and the second is finding the zeros of j=1nAj. To address the first problem, we produce fixed-point equations on the original Hilbert space as well as on the product space and find that these equations associate with crucial operators which are called generalized forward–backward splitting operators. To tackle the second problem, we point out that it can be reduced to a special instance of n=2 by defining new operators on the product space. Iterative schemes are given, which produce convergent sequences and these sequences ultimately lead to solutions for the last two problems. Full article
18 pages, 3022 KiB  
Article
Improvement and Application of Hale’s Dynamic Time Warping Algorithm
by Hairong Wang and Qiufang Zheng
Symmetry 2024, 16(6), 645; https://doi.org/10.3390/sym16060645 - 23 May 2024
Viewed by 602
Abstract
Due to the different generation and propagation mechanisms of P- and S-waves, there may be significant differences in the seismic data collected by the two, which poses a great obstacle to the time domain matching of P- and S-waves in multiwave exploration. Furthermore, [...] Read more.
Due to the different generation and propagation mechanisms of P- and S-waves, there may be significant differences in the seismic data collected by the two, which poses a great obstacle to the time domain matching of P- and S-waves in multiwave exploration. Furthermore, the quality and accuracy of the matching effect will directly affect the subsequent multiwave joint inversion and interpretation effect. Therefore, the study of P and S-wave-matching methods plays a crucial role in seismic exploration. In 2013, Hale improved the classical Dynamic Time Warping (DTW) algorithm applied to solve the problem of speech recognition, and obtained the DTW algorithm suitable for solving the matching of P-waves and S-waves. The seismic wave-matching results generated by this algorithm are horizontal discontinuous (different trajectories) and need further processing. This study analyses the algorithm based on simulations of seismic waves using Ricker wavelets. In response to existing problems, this paper proposes strategies to improve the DTW algorithm. The algorithm in this study significantly improved the continuity of the registration results of the actual seismic wave data in the horizontal direction (different traces). Full article
Show Figures

Figure 1

18 pages, 328 KiB  
Article
A Necessary Optimality Condition on the Control of a Charged Particle
by Nigar Yildirim Aksoy, Ercan Celik and Merve Zengin
Symmetry 2024, 16(6), 637; https://doi.org/10.3390/sym16060637 - 21 May 2024
Viewed by 603
Abstract
We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute [...] Read more.
We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality. Full article
35 pages, 542 KiB  
Article
An Optimal Control Perspective on Classical and Quantum Physical Systems
by Mauricio Contreras González, Marcelo Villena and Roberto Ortiz Herrera
Symmetry 2023, 15(11), 2033; https://doi.org/10.3390/sym15112033 - 8 Nov 2023
Cited by 1 | Viewed by 1021
Abstract
This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in [...] Read more.
This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels. Full article
Show Figures

Figure 1

16 pages, 339 KiB  
Article
Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement
by Abdelkader Braik, Safa M. Mirgani, Eltigani I. Hassan and Khaled Zennir
Symmetry 2023, 15(10), 1878; https://doi.org/10.3390/sym15101878 - 6 Oct 2023
Viewed by 1064
Abstract
In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on [...] Read more.
In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional. Full article
26 pages, 8514 KiB  
Article
Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation
by Marwa Hassan, Eman Beshr, Mahmoud Beshr and Ali M. El-Rifaie
Symmetry 2023, 15(9), 1661; https://doi.org/10.3390/sym15091661 - 28 Aug 2023
Viewed by 1170
Abstract
This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by [...] Read more.
This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by the optimization of the proportional derivative (PD) coefficients through the Adaptive Neuro-Fuzzy Inference System. In addition, the system’s reaction to harsh environments is managed using Long Short-Term Memory. In order to gain a deeper understanding, symmetrical environmental disturbances and trajectories are introduced during the testing phase. The results demonstrate the superior performance of the control strategy, with reduced vibrations, faster recovery and confirmed tracking accuracy. In addition, the control method shows its adaptability and reliability, as evidenced by the significant reduction in CO2 emissions compared to conventional PD control methods. The use of symmetric trajectories and visualizations further emphasizes the behavior of the system under symmetric conditions, strengthening the effectiveness and applicability of the control strategy in real-world scenarios. Overall, this study presents a promising solution for converting complex systems under different conditions and making them potentially applicable in various industrial contexts. Full article
Show Figures

Figure 1

17 pages, 522 KiB  
Article
Fuzzy Adaptive Parameter in the Dai–Liao Optimization Method Based on Neutrosophy
by Predrag S. Stanimirović, Branislav D. Ivanov, Dragiša Stanujkić, Lev A. Kazakovtsev, Vladimir N. Krutikov and Darjan Karabašević
Symmetry 2023, 15(6), 1217; https://doi.org/10.3390/sym15061217 - 7 Jun 2023
Viewed by 1161
Abstract
The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, [...] Read more.
The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, we suggest and explore a new neutrosophic logic system intended to compute the essential parameter t required in Dai–Liao CG iterations. Theoretical examination and numerical experiments signify the effectiveness of the introduced method for controlling t. By incorporation of the neutrosophy in the Dai–Liao conjugate gradient principle, we established novel Dai–Liao CG iterations for solving large-scale unconstrained optimization problems. Global convergence is proved under standard assumptions and with the use of the inexact line search. Finally, computational evidence shows the computational effectiveness of the proposed fuzzy neutrosophic Dai–Liao CG method. Full article
Show Figures

Figure 1

17 pages, 791 KiB  
Article
Classical Solutions for the Generalized Kawahara–KdV System
by Svetlin G. Georgiev, A. Boukarou, Keltoum Bouhali, Khaled Zennir, Hatim M. Elkhair, Eltegani I. Hassan, Alnadhief H. A. Alfedeel and Almonther Alarfaj
Symmetry 2023, 15(6), 1159; https://doi.org/10.3390/sym15061159 - 26 May 2023
Cited by 1 | Viewed by 1212
Abstract
In this article, we investigate the generalized Kawahara–KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are based upon recent theoretical results. Full article
Back to TopTop