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Symmetry
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Asymmetric and Symmetric Study on Applied Mathematics in ODE, PDE...
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Asymmetric and Symmetric Study on Applied Mathematics in ODE, PDE and FDE Model

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

Deadline for manuscript submissions: closed (15 April 2024) | Viewed by 2755

Special Issue Editors

Prof. Dr. Kaihong Zhao

E-Mail Website
Guest Editor
Department of Mathematics, School of Electronics & Information Engineering, Taizhou University, Taizhou 318000, China
Interests: ecological differential dynamical system; neural network system; fractional order dynamical system; functional differential equation; parabolic partial differential equation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Quanxin Zhu

grade E-Mail Website
Guest Editor
School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China
Interests: stochastic control; stochastic systems; stochastic stability; stochastic delayed systems; markovian jump systems; stochastic complex networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry and asymmetry are common in natural science and engineering technology, and even in social science. The theory and application of differential equations are an important part of Applied Mathematics. The main application field of differential equations in physics. Therefore, the symmetric and asymmetric dynamic characteristics that are common in physics are studied through their corresponding differential equation models. However, the purpose of this Special Issue is to provide a platform for scholars to exchange research work on symmetry and asymmetry in other disciplines besides physical chemistry, such as biological ecosystem, neural network system, epidemic dynamic system, economic and financial dynamic system, etc., by applying the theory and methods of differential equations and dynamic systems. The main objectives and scopes of this Special Issue (including but not limited to) are as follows:

  1. Studies on symmetry and asymmetry in the ODE model;
  2. Studies on symmetry and asymmetry in the PDE model;
  3. Studies on symmetry and asymmetry in the FDE model.

Prof. Dr. Kaihong Zhao
Prof. Dr. Quanxin Zhu
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

  • biological ecosystem
  • neural network system
  • epidemic dynamic system
  • qualitative and stability
  • symmetry and asymmetry

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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

13 pages, 7840 KiB  
Article
Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions
by Xiaojun Lv, Kaihong Zhao and Haiping Xie
Symmetry 2024, 16(6), 774; https://doi.org/10.3390/sym16060774 - 20 Jun 2024
Cited by 2 | Viewed by 969
Abstract
The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for [...] Read more.
The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for differential equations and have wide applications. Therefore, this article considers a class of nonlinear Hadamard fractional coupling (p1,p2)-Laplacian systems with periodic boundary value conditions. Based on nonlinear analysis methods and the contraction mapping principle, we obtain some new and easily verifiable sufficient criteria for the existence and uniqueness of solutions to this system. Moreover, we further discuss the generalized Ulam–Hyers (GUH) stability of this problem by using some inequality techniques. Finally, three examples and simulations explain the correctness and availability of our main results. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Applied Mathematics in ODE, PDE and FDE Model)
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11 pages, 279 KiB  
Article
Positive Periodic Solutions for a First-Order Nonlinear Neutral Differential Equation with Impulses on Time Scales
by Shihong Zhu and Bo Du
Symmetry 2023, 15(5), 1072; https://doi.org/10.3390/sym15051072 - 12 May 2023
Viewed by 1040
Abstract
In this article, we discuss the existence of a positive periodic solution for a first-order nonlinear neutral differential equation with impulses on time scales. Based on the Leggett–Williams fixed-point theorem and Krasnoselskii’s fixed-point theorem, some sufficient conditions are established for the existence of [...] Read more.
In this article, we discuss the existence of a positive periodic solution for a first-order nonlinear neutral differential equation with impulses on time scales. Based on the Leggett–Williams fixed-point theorem and Krasnoselskii’s fixed-point theorem, some sufficient conditions are established for the existence of positive periodic solution. An example is given to show the feasibility and application of the obtained results. Since periodic solutions are solutions with symmetry characteristics, the existence conditions for periodic solutions also imply symmetry. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Applied Mathematics in ODE, PDE and FDE Model)
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