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Axioms
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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 August 2026 | Viewed by 3394

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 250 words) can be sent to the Editorial Office for assessment.

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

Related Special Issue

Published Papers (5 papers)

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Research

18 pages, 4391 KB  
Article
Studying Chaos in a Modified Dynamical Model: Some Applications
by Tsvetelin Zaevski, Nikolay Kyurkchiev, Anton Iliev, Vesselin Kyurkchiev and Asen Rahnev
Axioms 2026, 15(5), 327; https://doi.org/10.3390/axioms15050327 - 30 Apr 2026
Viewed by 107
Abstract
Many authors consider modified SIQR (susceptible, infected, isolated (quarantined), and recovered individuals) models for childhood diseases. In this paper, we examine a modified differential system with N free parameters that may be of interest to epidemiology experts. We pay special attention to the [...] Read more.
Many authors consider modified SIQR (susceptible, infected, isolated (quarantined), and recovered individuals) models for childhood diseases. In this paper, we examine a modified differential system with N free parameters that may be of interest to epidemiology experts. We pay special attention to the Melnikov function, which corresponds to the proposed new model. We create the Melnikov equation (M(t)=0) and analyze all of its roots using a specially designed software program. This gives the researcher the chance to accurately comprehend and articulate the classical Melnikov criterion for the potential appearance of chaos in the dynamical system. Additionally, we present a few specific modules for examining the new model’s dynamics. Additionally covered is a potential use of the Melnikov function that corresponds to the differential model under consideration, with particular potential in the modeling and synthesis of antenna diagrams. Last but not least, we consider the proposed generalization from a stochastic point of view. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition)
21 pages, 1731 KB  
Article
A Computational Analysis of Nonlinear Fractional Coupled System of Boussinesq–Burger Equations with the Non-Singular Kernel
by Mashael M. AlBaidani and Rabab Alzahrani
Axioms 2026, 15(3), 172; https://doi.org/10.3390/axioms15030172 - 28 Feb 2026
Viewed by 325
Abstract
The coupled nonlinear system of fractional Boussinesq–Burger equations that may be utilized to model the propagation of shallow water waves is solved in this study using a novel numerical approach. The fractional derivatives in Caputo–Fabrizio and Atangana–Baleanu manner are executed in the system [...] Read more.
The coupled nonlinear system of fractional Boussinesq–Burger equations that may be utilized to model the propagation of shallow water waves is solved in this study using a novel numerical approach. The fractional derivatives in Caputo–Fabrizio and Atangana–Baleanu manner are executed in the system under consideration. The exact solutions of the proposed nonlinear fractional system are shown in the classical scenario of fractional order at ß=1, whereas the approximate solutions are derived using the natural decomposition method. The series solution is generated such that it is simple to compute. Our results are compared with the exact results which clearly show that the suggested approach solutions quickly converge to the known accurate results. We acquire some analysis of the absolute error by comparing the approximate values with their corresponding precise solutions throughout the provided computations. Numerical and graphical simulations are used to confirm the usefulness of the suggested approach, and the outcomes are compared with well-known methods like the fractional decomposition method (FDM) and Laplace residual power series method (LRPSM). It is evident from the comparison that our approach offers better outcomes compared to other approaches. The results of the suggested method are very accurate and give helpful details on the real dynamics of the proposed system. The obtained outcomes ensure that the suggested approach is more effective and examines the highly nonlinear problems arising in engineering and science. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition)
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11 pages, 219 KB  
Article
Double Wronskian Representation of the Nth-Order Solutions to the Davey–Stewartson Equations
by Pierre Gaillard
Axioms 2025, 14(11), 799; https://doi.org/10.3390/axioms14110799 - 30 Oct 2025
Viewed by 451
Abstract
Solutions to the Davey–Stewartson equations (DS) in terms of the determinants of order 2N depending on 4N real parameters are constructed. The Darboux transformation is used to construct solutions of order N to this equation. We obtain a representation of the [...] Read more.
Solutions to the Davey–Stewartson equations (DS) in terms of the determinants of order 2N depending on 4N real parameters are constructed. The Darboux transformation is used to construct solutions of order N to this equation. We obtain a representation of the solutions to the equations (DS) in terms of two Wronskians. We obtain what we call a double Wronskian representation of the solutions to the (DS) equations. With this method, some particular explicit solutions for the first orders are constructed. Full article
(This article belongs to the Special Issue Differential Equations and Dynamical Systems: Theory and Applications, 2nd Edition)
16 pages, 820 KB  
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 822
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 KB  
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
Cited by 1 | Viewed by 719
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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