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Symmetry
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Symmetry and Asymmetry in Nonlinear Systems
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Symmetry and Asymmetry in Nonlinear Systems

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

Deadline for manuscript submissions: 31 May 2025 | Viewed by 3277

Special Issue Editors

Prof. Dr. Brouri Adil

E-Mail Website
Guest Editor
ENSAM, Moulay Ismail University, Meknes, Morocco
Interests: identification and control of non-linear systems; renewable energies
Dr. Abdelmalek Ouannou

E-Mail Website
Guest Editor
ENSAM-Meknes, Moulay Ismail University, Meknes, Morocco
Interests: MATLAB simulation; mechatronics; automation; electrical power engineering; control and instrumentation
Prof. Dr. Sorin Vlase

E-Mail Website
Guest Editor
Department of Mechanics, “Transilvania” University of Brasov, Brasov, Romania
Interests: mechanics; vibrations; elasticity; composite materials; analytical mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Generally, industrial systems behave as nonlinear systems. Although several studies on the identification and control of systems have focused on linear systems, several problems regarding the identification and control of nonlinear systems remain. Linear systems can be regarding as special cases of nonlinear or bilinear systems. In this Special Issue, particular attention will be paid to the identification and control of nonlinear systems, with the considered nonlinearities being either static or dynamic, e.g., backlash, switch, hysteresis, or other nonlinearity types.

In this Special Issue, we welcome the submission of articles addressing nonlinear systems structured in blocks (with linear and nonlinear blocks).

System controls are widely utilized in the industrial sector. Therefore, in this Special Issue, we also welcome contributions that propose techniques with the potential to control nonlinear systems using backstepping, Lyapunov functions or functionals, sliding mode, and adaptive control.

Prof. Dr. Brouri Adil
Dr. Abdelmalek Ouannou
Prof. Dr. Sorin Vlase
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 systems
  • bilinear systems
  • control
  • identification
  • stability
  • backlash
  • hysteresis

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Published Papers (4 papers)

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Research

21 pages, 7863 KiB  
Article
Enhancement of Thermomechanical Protocol for Automotive Brake Using the Symmetry of the Disc: Numerical Validation and Material Selection
by Mohammed Berrada Gouzi, Ali Hajjia, Ahmed El Khalfi, Bilal Harras, Sorin Vlase and Maria Luminita Scutaru
Symmetry 2025, 17(2), 289; https://doi.org/10.3390/sym17020289 - 13 Feb 2025
Viewed by 585
Abstract
In the context of the automotive industry, this paper proposes an enhancement of the numerical simulation using FEM and performing material choosing with the Ashby method for automotive brake discs, using the symmetric shape of the disc. Automotive braking involves the dissipation of [...] Read more.
In the context of the automotive industry, this paper proposes an enhancement of the numerical simulation using FEM and performing material choosing with the Ashby method for automotive brake discs, using the symmetric shape of the disc. Automotive braking involves the dissipation of kinetic energy through heat generation due to friction, a physical phenomenon that alters the mechanical properties of brake discs. This prompts automotive development engineers to investigate new materials capable of absorbing heat while maintaining their mechanical properties. A thermomechanical study of a ventilated front brake disc has successfully demonstrated a good performance of cast iron because the equivalent stress is significantly lower than the elastic limit, with a margin of approximately 73 MPa. Compared to validated results extracted from the state of the art, the adopted methodology gives more realistic results with minimum CPU requirements, where the total time of calculation is around 40 min. More than that, the results are suitable to be used for studying durability and other properties like mechanical impact and fatigue. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)
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15 pages, 298 KiB  
Article
Symmetry Properties and Their Application to Hilfer Fractional Systems
by Beata Sikora
Symmetry 2025, 17(2), 288; https://doi.org/10.3390/sym17020288 - 13 Feb 2025
Viewed by 416
Abstract
The paper investigates semilinear Hilfer fractional systems. A symmetric fractional derivative and its properties are discussed. A symmetrized model for these systems is proposed and examined. A bounded nonlinear function f is applied, depending on the time as well as on the state. [...] Read more.
The paper investigates semilinear Hilfer fractional systems. A symmetric fractional derivative and its properties are discussed. A symmetrized model for these systems is proposed and examined. A bounded nonlinear function f is applied, depending on the time as well as on the state. The Laplace transformation is used to derive the solution formula for the systems under consideration. The primary contribution of the paper is the formulation and proof of controllability criteria for symmetrized Hilfer systems. To deepen the understanding of the dynamics of such systems, the concept of reflection symmetries is introduced with a detailed analysis of their essential features, including projection functions and a reflection operator. Furthermore, a decomposition of the symmetric Hilfer fractional derivative is presented, utilizing the projection function and reflection operator. This decomposition not only provides a controllability condition for symmetrized Hilfer systems but also clarifies the relationship between the system’s trajectory across subintervals. Two illustrative examples are presented to demonstrate the computational and practical significance of the theoretical results. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)
17 pages, 440 KiB  
Article
Frobenius Norm-Based Global Stability Analysis of Delayed Bidirectional Associative Memory Neural Networks
by N. Mohamed Thoiyab, Saravanan Shanmugam, Rajarathinam Vadivel and Nallappan Gunasekaran
Symmetry 2025, 17(2), 183; https://doi.org/10.3390/sym17020183 - 24 Jan 2025
Viewed by 979
Abstract
The present research investigates the global asymptotic stability of bidirectional associative memory (BAM) neural networks using distinct sufficient conditions. The primary objective of this study is to establish new generalized criteria for the global asymptotic robust stability of time-delayed BAM neural networks at [...] Read more.
The present research investigates the global asymptotic stability of bidirectional associative memory (BAM) neural networks using distinct sufficient conditions. The primary objective of this study is to establish new generalized criteria for the global asymptotic robust stability of time-delayed BAM neural networks at the equilibrium point, utilizing the Frobenius norm and the positive symmetrical approach. The new sufficient conditions are derived with the help of the Lyapunov–Krasovskii functional and the Frobenius norm, which are important in deep learning for a variety of reasons. The derived conditions are not influenced by the system parameter delays of the BAM neural network. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed conclusions regarding network parameters. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)
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30 pages, 474 KiB  
Article
Symmetry and Complexity in Gene Association Networks Using the Generalized Correlation Coefficient
by Raydonal Ospina, Cleber M. Xavier, Gustavo H. Esteves, Patrícia L. Espinheira, Cecilia Castro and Víctor Leiva
Symmetry 2024, 16(11), 1510; https://doi.org/10.3390/sym16111510 - 11 Nov 2024
Viewed by 706
Abstract
High-dimensional gene expression data cause challenges for traditional statistical tools, particularly when dealing with non-linear relationships and outliers. The present study addresses these challenges by employing a generalized correlation coefficient (GCC) that incorporates a flexibility parameter, allowing it to adapt to varying levels [...] Read more.
High-dimensional gene expression data cause challenges for traditional statistical tools, particularly when dealing with non-linear relationships and outliers. The present study addresses these challenges by employing a generalized correlation coefficient (GCC) that incorporates a flexibility parameter, allowing it to adapt to varying levels of symmetry and asymmetry in the data distribution. This adaptability is crucial for analyzing gene association networks, where the GCC demonstrates advantages over traditional measures such as Kendall, Pearson, and Spearman coefficients. We introduce two novel adaptations of this metric, enhancing its precision and broadening its applicability in the context of complex gene interactions. By applying the GCC to relevance networks, we show how different levels of the flexibility parameter reveal distinct patterns in gene interactions, capturing both linear and non-linear relationships. The maximum likelihood and Spearman-based estimators of the GCC offer a refined approach for disentangling the complexity of biological networks, with potential implications for precision medicine. Our methodology provides a powerful tool for constructing and interpreting relevance networks in biomedicine, supporting advancements in the understanding of biological interactions and healthcare research. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Systems)
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