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Symmetry
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Symmetry in Mathematical Modelling: Topics and Advances
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Symmetry in Mathematical Modelling: Topics and Advances

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 4572

Special Issue Editors

Dr. Xiao-Bao Shu

E-Mail Website
Guest Editor
College of Mathematics, Hunan University, Changsha 410012, China
Interests: impulsive differential equation; stochastic differential equation; optimization problem; fractional differential equation
Special Issues, Collections and Topics in MDPI journals
Dr. Fei Xu

E-Mail Website
Guest Editor
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada
Interests: biomathematics; evolutionary game theory; nonlinear dynamics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As a universal phenomenon in nature, symmetry has attracted the attention of scholars. Symmetry has been found in physics, chemistry, biology, finance, and mathematics. The study of symmetry provides insights into these subjects. Mathematical models are an important method of studying real-world systems. The symmetry reflected by such mathematical models reveals the inherent symmetry of real-world systems. It is of practical significance to study such symmetry phenomena. Many directions of mathematics involve symmetry problems. For example, chaotic attractors often display symmetric topology. Many systems of differential equations, such as impulsive differential equations, stochastic impulsive differential equations, and fractional differential equations, also have symmetry properties. Moreover, many models based on game theory exhibit symmetry.

The aim of this Special Issue is to provide a platform for scholars to present the latest research on mathematical modelling related to symmetry.

The topics of interest for this Special Issue include but are not limited to mathematical modelling, nonlinear dynamics, ordinary differential equations, partial differential equations, impulsive differential equations, random impulsive differential equations, biomathematics, financial mathematics, chaos, artificial intelligence, machine learning, neural networks, and data analysis.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Symmetry in Mathematical Modelling: Topics and Advances” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Xiao-Bao Shu
Prof. Dr. Fei Xu
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
  • Mathematical modelling
  • Ordinary differential equations
  • Partial differential equations
  • Impulsive differential equations
  • Random impulsive differential equations
  • Nonlinear dynamics
  • Biomathematics
  • Financial mathematics
  • Chaos
  • Artificial intelligence
  • Machine learning
  • Neural network
  • Data analysis

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

Published Papers (2 papers)

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Research

22 pages, 2119 KiB  
Article
On Performance of Marine Predators Algorithm in Training of Feed-Forward Neural Network for Identification of Nonlinear Systems
by Ceren Baştemur Kaya
Symmetry 2023, 15(8), 1610; https://doi.org/10.3390/sym15081610 - 20 Aug 2023
Cited by 3 | Viewed by 1105
Abstract
Artificial neural networks (ANNs) are used to solve many problems, such as modeling, identification, prediction, and classification. The success of ANN is directly related to the training process. Meta-heuristic algorithms are used extensively for ANN training. Within the scope of this study, a [...] Read more.
Artificial neural networks (ANNs) are used to solve many problems, such as modeling, identification, prediction, and classification. The success of ANN is directly related to the training process. Meta-heuristic algorithms are used extensively for ANN training. Within the scope of this study, a feed-forward artificial neural network (FFNN) is trained using the marine predators algorithm (MPA), one of the current meta-heuristic algorithms. Namely, this study is aimed to evaluate the performance of MPA in ANN training in detail. Identification/modeling of nonlinear systems is chosen as the problem. Six nonlinear systems are used in the applications. Some of them are static, and some are dynamic. Mean squared error (MSE) is utilized as the error metric. Effective training and testing results were obtained using MPA. The best mean error values obtained for six nonlinear systems are 2.3 × 10−4, 1.8 × 10−3, 1.0 × 10−4, 1.0 × 10−4, 1.2 × 10−5, and 2.5 × 10−4. The performance of MPA is compared with 16 meta-heuristic algorithms. The results have shown that the performance of MPA is better than other algorithms in ANN training for the identification of nonlinear systems. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Modelling: Topics and Advances)
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14 pages, 2319 KiB  
Article
Application of Bat Algorithm and Its Modified Form Trained with ANN in Channel Equalization
by Pradyumna Kumar Mohapatra, Saroja Kumar Rout, Sukant Kishoro Bisoy, Sandeep Kautish, Muzaffar Hamzah, Muhammed Basheer Jasser and Ali Wagdy Mohamed
Symmetry 2022, 14(10), 2078; https://doi.org/10.3390/sym14102078 - 6 Oct 2022
Cited by 16 | Viewed by 2206
Abstract
The transmission of high-speed data over communication channels is the function of digital communication systems. Due to linear and nonlinear distortions, data transmitted through this process is distorted. In a communication system, the channel is the medium through which signals are transmitted. The [...] Read more.
The transmission of high-speed data over communication channels is the function of digital communication systems. Due to linear and nonlinear distortions, data transmitted through this process is distorted. In a communication system, the channel is the medium through which signals are transmitted. The useful signal received at the receiver becomes corrupted because it is associated with noise, ISI, CCI, etc. The equalizers function at the front end of the receiver to eliminate these factors, and they are designed to make them work efficiently with proper network topology and parameters. In the case of highly dispersive and nonlinear channels, it is well known that neural network-based equalizers are more effective than linear equalizers, which use finite impulse response filters. An alternative approach to training neural network-based equalizers is to use metaheuristic algorithms. Here, in this work, to develop the symmetry-based efficient channel equalization in wireless communication, this paper proposes a modified form of bat algorithm trained with ANN for channel equalization. It adopts a population-based and local search algorithm to exploit the advantages of bats’ echolocation. The foremost initiative is to boost the flexibility of both the variants of the proposed algorithm and the utilization of proper weight, topology, and the transfer function of ANN in channel equalization. To evaluate the equalizer’s performance, MSE and BER can be calculated by considering popular nonlinear channels and adding nonlinearities. Experimental and statistical analyses show that, in comparison with the bat as well as variants of the bat and state-of-the-art algorithms, the proposed algorithm substantially outperforms them significantly, based on MSE and BER. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Modelling: Topics and Advances)
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