Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Research on Dynamical Systems and Differential Equations, 2nd Edition
share announcement

Research on Dynamical Systems and Differential Equations, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 2025

Special Issue Editors

Dr. Ahmadjan Muhammadhaji

E-Mail Website
Guest Editor
1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
2. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China
Interests: differential equation; dynamical systems
Special Issues, Collections and Topics in MDPI journals
Dr. Maimaiti Yimamu

E-Mail Website
Guest Editor
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Interests: differential equation; dynamical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Dynamical systems and differential equations are fundamental areas of mathematics that have been applied across a wide range of fields, including physics, chemistry, engineering, biology, economics, electronics, ecology, epidemiology, neural networks, and many other real-world domains. Dynamical systems refer to a collection of mathematical models that describe the time evolution of physical or abstract systems. Differential equations, on the other hand, are mathematical equations that describe the relationship between a function and its derivatives.

Overall, dynamical systems and differential equations comprise a vibrant and active field with numerous applications and exciting open problems.

Therefore, this Special Issue aims to collate findings of mathematicians, biologists, physicists, epidemiologists, engineers, economists, ecologists, mechanists, and other scientists for whom dynamical systems and differential equations are valuable research tools.

Dr. Ahmadjan Muhammadhaji
Dr. Maimaiti Yimamu
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 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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • differential equations
  • deterministic and stochastic differential equations
  • dynamical systems
  • modeling and dynamics in population dynamical systems
  • complex networks
  • neural networks
  • epidemic models
  • disease modeling
  • stochastic processes and their applications
  • statistical models and algorithms
  • stochastic models in biology

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Related Special Issue

Published Papers (4 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

15 pages, 429 KB  
Article
Algebraic Reduction and Periodic Solvability in a Coupled Ternary Rational System
by Ahmed Ghezal, Ahmed A. Al Ghafli and Hassan J. Al Salman
Mathematics 2026, 14(8), 1396; https://doi.org/10.3390/math14081396 - 21 Apr 2026
Viewed by 130
Abstract
In this paper, we investigate a new class of three-component nonlinear rational difference equations of the second order characterized by structured periodic interactions. Through a carefully designed algebraic transformation and the introduction of suitable auxiliary sequences, the original nonlinear model is converted into [...] Read more.
In this paper, we investigate a new class of three-component nonlinear rational difference equations of the second order characterized by structured periodic interactions. Through a carefully designed algebraic transformation and the introduction of suitable auxiliary sequences, the original nonlinear model is converted into an equivalent periodic scheme of order six. This reformulation enables the complete determination of explicit solution formulas in closed form. We establish precise conditions under which the solutions remain well defined and analytically tractable. A series of illustrative numerical experiments reveals a wide spectrum of dynamical behaviors, ranging from oscillatory patterns to various modes of convergence. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations, 2nd Edition)
►▼ Show Figures

Figure 1

28 pages, 5984 KB  
Article
Threshold Dynamics of Within-Host CHIKV Infection: A Delay Differential Equation Model with Persistent Infected Monocytes and Humoral Immunity
by Mohammed H. Alharbi and Ali Rashash Alzahrani
Mathematics 2026, 14(8), 1331; https://doi.org/10.3390/math14081331 - 15 Apr 2026
Viewed by 174
Abstract
In this paper, we present a mathematical analysis of within-host CHIKV dynamics by developing and studying a novel delay differential equation model that incorporates persistent infected monocytes, discrete time delays, and an antibody-mediated humoral immune response. The model includes five compartments: susceptible monocytes, [...] Read more.
In this paper, we present a mathematical analysis of within-host CHIKV dynamics by developing and studying a novel delay differential equation model that incorporates persistent infected monocytes, discrete time delays, and an antibody-mediated humoral immune response. The model includes five compartments: susceptible monocytes, persistent infected monocytes, actively infected monocytes, CHIKV pathogens, and neutralizing antibodies. To reflect key biological latencies, we introduce four distinct discrete delays accounting for the periods between viral entry and the emergence of infected cell populations, intracellular virion production, and antibody activation. We analyze the model, establishing the positivity, boundedness, and invariance of solutions, and derive the basic reproduction number R0 via the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, we prove a threshold dynamic: the infection-free equilibrium is globally asymptotically stable (GAS) when R0≤1, while a unique endemic equilibrium is GAS when R0>1. Numerical simulations validate the analytical results and illustrate threshold behavior. A detailed local sensitivity analysis of R0 identifies the most influential parameters, offering theoretical insights into potential intervention strategies. We further investigate the effects of antiviral therapy as a theoretical intervention, deriving a treatment-dependent reproduction number and the critical drug efficacy required for eradication, and explore how the intracellular production delay can itself serve as a critical threshold for infection clearance. The study provides a rigorous theoretical framework that highlights the roles of latency, immune response, and biological delays in CHIKV pathogenesis and offers qualitative insights that may inform future experimental and treatment design studies. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations, 2nd Edition)
►▼ Show Figures

Figure 1

16 pages, 313 KB  
Article
Unified Counterexamples to Endpoint Regularity for Linear Elliptic Equations with Singular Coefficients
by Haesung Lee
Mathematics 2026, 14(7), 1130; https://doi.org/10.3390/math14071130 - 27 Mar 2026
Viewed by 339
Abstract
This paper presents unified counterexamples for which standard elliptic regularity results break down for linear elliptic equations with highly singular coefficients in dimensions d≥3. First, we establish well-posedness for the case where the drift vector field has merely L2 [...] Read more.
This paper presents unified counterexamples for which standard elliptic regularity results break down for linear elliptic equations with highly singular coefficients in dimensions d≥3. First, we establish well-posedness for the case where the drift vector field has merely L2-integrability but can be expressed as the gradient of a bounded potential function. Subsequently, we investigate the critical endpoint cases of known regularity results where coefficients or data satisfy borderline integrability conditions. By using a single, explicit function, ρ(x)=ln(2+1∥x∥), we present counterexamples to the regularity of solutions for divergence form equations and stationary Fokker–Planck equations. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations, 2nd Edition)
31 pages, 521 KB  
Article
Bayesian Analysis of Nonlinear Quantile Structural Equation Model with Possible Non-Ignorable Missingness
by Lu Zhang and Mulati Tuerde
Mathematics 2025, 13(19), 3094; https://doi.org/10.3390/math13193094 - 26 Sep 2025
Cited by 1 | Viewed by 774
Abstract
This paper develops a nonlinear quantile structural equation model via the Bayesian approach, aiming to more accurately analyze the relationships between latent variables, with special attention paid to the issue of non-ignorable missing data in the model. The model not only incorporates quantile [...] Read more.
This paper develops a nonlinear quantile structural equation model via the Bayesian approach, aiming to more accurately analyze the relationships between latent variables, with special attention paid to the issue of non-ignorable missing data in the model. The model not only incorporates quantile regression to examine the relationships between latent variables at different quantile levels but also features a specially designed mechanism for handling missing data. The non-ignorable missing mechanism is specified through a logistic regression model, and a combined method of Gibbs sampling and Metropolis–Hastings sampling is adopted for missing value imputation, while simultaneously estimating unknown parameters, latent variables, and parameters in the missing data model. To verify the effectiveness of the proposed method, simulation studies are conducted under conditions of different sample sizes and missing rates. The results of these simulation studies indicate that the developed method performs excellently in handling complex data structures and missing data. Furthermore, this paper demonstrates the practical application value of the nonlinear quantile structural equation model through a case study on the growth of listed companies, providing researchers in related fields with a new analytical tool. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations, 2nd Edition)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop