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Axioms
Special Issues
Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition
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Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1040

Special Issue Editor

Dr. Nicolae Lupa

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Guest Editor
Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
Interests: stability theory of dynamical systems; nonuniform behavior; well-posed evolution equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is well known that dynamical systems have a lot of applications in modeling the dynamics of many real-life phenomena and processes, including physics, chemistry, engineering, life sciences, economic, etc.

In the stability theory of linear dynamical systems, a central problem is finding conditions for the existence of stability, dichotomy, or trichotomy of their solutions.

This Special Issue of Axioms deals with the stability theory of continuous and discrete dynamical systems and their advanced applications. Original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Ordinary differential equations;
  • Partial differential equations;
  • Delay differential equations;
  • Fractional differential equations;
  • Functional equations;
  • Integral equations;
  • Impulsive equations;
  • Dynamical systems on time scales;
  • Difference equations;
  • Stochastic processes.

I look forward to receiving your contributions.

Dr. Nicolae Lupa
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. Axioms 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

  • dynamical systems
  • differential equations
  • difference equations
  • functional equations
  • integral equations
  • evolution families
  • semigroups
  • asymptotic behavior
  • stability
  • dichotomy
  • trichotomy
  • Lyapunov functions

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Related Special Issue

Published Papers (2 papers)

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Research

16 pages, 820 KiB  
Article
Stability Analysis of SEIAR Model with Age Structure Under Media Effect
by Hongliang Gao, Fanli Zhang and Jiemei Li
Axioms 2025, 14(6), 412; https://doi.org/10.3390/axioms14060412 - 28 May 2025
Viewed by 177
Abstract
In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected [...] Read more.
In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number R0, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when R0<1, the disease-free equilibrium is globally asymptotically stable; (2) when R0>1, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition)
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14 pages, 409 KiB  
Article
Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications
by Mouataz Billah Mesmouli, Abdelouaheb Ardjouni, Ioan-Lucian Popa, Hicham Saber, Faten H. Damag, Yasir A. Madani and Taher S. Hassan
Axioms 2025, 14(4), 269; https://doi.org/10.3390/axioms14040269 - 2 Apr 2025
Viewed by 298
Abstract
Neutral transmission line models are essential for analyzing stability and periodicity in systems influenced by nonlinear and delayed dynamics, particularly in modern smart grids. This study utilizes Krasnoselskii’s fixed-point theorem to establish sufficient conditions for the existence and asymptotic stability of periodic solutions, [...] Read more.
Neutral transmission line models are essential for analyzing stability and periodicity in systems influenced by nonlinear and delayed dynamics, particularly in modern smart grids. This study utilizes Krasnoselskii’s fixed-point theorem to establish sufficient conditions for the existence and asymptotic stability of periodic solutions, eliminating the need for differentiability in delay terms and coefficients. The results extend existing findings and are validated through a single test example, demonstrating the theoretical applicability of the proposed approach. These findings provide a mathematical framework for understanding the behavior of power distribution systems under nonlinear and delayed influences. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition)
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