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Applied Mathematical Modelling and Dynamical Systems, 2nd Edition
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Applied Mathematical Modelling and Dynamical Systems, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 4517

Special Issue Editors

Prof. Dr. José Leonel Linhares da Rocha

E-Mail Website
Guest Editor
CEAUL and Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Interests: nonlinear dynamics; population dynamics (Allee effects); bifurcation theory; networks; synchronization and applications
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Daniele Fournier-Prunaret

E-Mail Website
Guest Editor
Institut National des Sciences Appliquées de Toulouse, 31400 Toulouse, France
Interests: nonlinear systems; complex behaviours; bifurcations; chaos
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are delighted to announce the forthcoming opening of the second volume of our Special Issue. Building upon the resounding success of the inaugural edition, we present to you a renewed opportunity to contribute to a Special Issue titled "Applied Mathematical Modelling and Dynamical Systems, 2nd Edition".

In our ever-evolving society, numerous challenges are being resolved through the construction of intricate bridges that unite diverse branches of mathematics. From the abstract realms of theory to the practicality of equations, from intricate nonlinear systems to iterative processes, and from chaotic events to linear phenomena, the significance of forging connections between different fields has became evident. Such connections often give rise to remarkable theories that, when applied, wield the potential to enhance the human experience.

Dynamical systems serve as versatile models that can encapsulate a wide array of natural and societal phenomena. The core objective of theoretical exploration lies in the analysis and comprehension of processes that frequently intersect with diverse areas of application, encompassing fields such as control theory, bifurcation theory, population dynamics, networks, synchronization phenomena, electronics, physics, mechanics, economics, biology, and ecology, among many others.

In this second volume, we call for original research articles, concise communications, and comprehensive review papers. Our interests span across both theoretical inquiries and practical investigations into models associated with the aforementioned domains. We eagerly anticipate your contributions as we embark on this new chapter of exploration.

Prof. Dr. José Leonel Linhares da Rocha
Prof. Dr. Daniele Fournier-Prunaret
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. 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

  • mathematical modeling
  • dynamical systems
  • nonlinear systems
  • theory of singularities
  • fixed point theory
  • bifurcation theory
  • complex systems
  • iteration theory
  • topological dynamics
  • ergodic theory
  • symbolic dynamics
  • population dynamics
  • embedding problems
  • networks
  • synchronization
  • simulation
  • chaos
  • functional equations

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Related Special Issue

Published Papers (6 papers)

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Research

18 pages, 329 KiB  
Article
Measure-Theoretic Analysis of Stochastic Competence Sets and Dynamic Shapley Values in Banach Spaces
by Jih-Jeng Huang and Chin-Yi Chen
Mathematics 2024, 12(19), 3085; https://doi.org/10.3390/math12193085 - 1 Oct 2024
Viewed by 372
Abstract
We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path [...] Read more.
We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path continuity and moment estimates. The dynamic Shapley value is rigorously defined as a càdlàg stochastic process with an axiomatic characterization. We derive a martingale representation for this process and establish its asymptotic properties, including a strong law of large numbers and a functional central limit theorem under α-mixing conditions. This framework provides a rigorous basis for analyzing dynamic value attribution in abstract spaces, with potential applications to economic and game-theoretic models. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
15 pages, 549 KiB  
Article
Dynamics of Activation and Regulation of the Immune Response to Attack by Viral Pathogens Using Mathematical Modeling
by Ledyz Cuesta-Herrera, Luis Pastenes, Ariel D. Arencibia, Fernando Córdova-Lepe and Cristhian Montoya
Mathematics 2024, 12(17), 2681; https://doi.org/10.3390/math12172681 - 28 Aug 2024
Viewed by 615
Abstract
In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory [...] Read more.
In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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24 pages, 19259 KiB  
Article
Synergistic Exploration of Heat Transfer for Integration Magnetohydrodynamics of Nanofluids Peristaltic Transport within Annular Tubes
by Muhammad Magdy, Ramzy Abumandour, Islam Eldesoky and Hammad Alotaibi
Mathematics 2024, 12(13), 2024; https://doi.org/10.3390/math12132024 - 29 Jun 2024
Viewed by 638
Abstract
The problem of treating cancer is considered one of the most important daily challenges that affect the lives of people with cancer. This research deals with solving this problem theoretically. Through previous studies, it has been proven that gold nanoparticles are able to [...] Read more.
The problem of treating cancer is considered one of the most important daily challenges that affect the lives of people with cancer. This research deals with solving this problem theoretically. Through previous studies, it has been proven that gold nanoparticles are able to remove these cancer cells. The idea of this research is theoretically based on injecting a cancer patient with gold nanoparticles that are exposed to a magnetic field. When these particles penetrate cancerous cells and are exposed to a magnetic field, this causes their temperature to rise. The high temperature of the nanometer gold particles that penetrate the cells of the affected body leads to the explosion of the cancer cells. In this research, the various external forces that affect the flow movement of the nanofluid are studied and how its physical and thermal properties are affected by those external forces. The MHD peristaltic flow of a nanofluid in an annulus pipe as a result of the effect of the wall properties has been investigated. This has been achieved through slip and thermal conditions. Wave velocity u0 leads to flow development. The inner annulus wall is rigid, while the outer wall of the artery moves under the influence of wave peristaltic movement. The nonlinear equations that describe the flow are solved under long-wavelength assumptions. The results were compared with other numerical methods, such as finite volume and finite element and the long wavelength method and proved to be accurate and effective. The expressions of pressure difference, velocity, stream function, wall shear stress, and temperature are analyzed. It is noted that the flow velocity increases with the Knudsen number, and the increased source heat suggests an increased temperature. The increasing amplitude ratio at most of the interface points between the artery wall and the catheter results in increased velocity. The streamlines are affected by the magnetic field, as increasing the influencing magnetic field leads to a decrease in flow lines. It is observed that this stress decreases when nanoparticles increase, in contrast to the effect of the magnetic field and also the occurrence of slipping. It was found that the mass of the wall cells relative to their area works to decrease the pressure difference, in contrast to the tension between those cells, which works to increase the pressure difference. Without slipping Kn=0 and with slipping Kn=0.1, the temperature decreases with increasing in nanoparticle concentration φ. The temperature also increases with the amplitude ratio δ. This strongly affects the generated drag on the catheter wall, which is mainly responsible for the enhanced temperature on this wall. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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25 pages, 1075 KiB  
Article
Lambert W Functions in the Analysis of Nonlinear Dynamics and Bifurcations of a 2D γ-Ricker Population Model
by J. Leonel Rocha, Abdel-Kaddous Taha and Stella Abreu
Mathematics 2024, 12(12), 1805; https://doi.org/10.3390/math12121805 - 10 Jun 2024
Viewed by 564
Abstract
The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ-Ricker population model. Through the use of such transcendental functions, it is possible to study the [...] Read more.
The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ-Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter γ is even or odd. In addition, the analysis of the bifurcation structure of this γ-Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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16 pages, 1032 KiB  
Article
Global Dynamics in an Alcoholism Epidemic Model with Saturation Incidence Rate and Two Distributed Delays
by Zejun Wang, Haicheng Liu, Mingyang Li and Mei Yang
Mathematics 2023, 11(24), 4870; https://doi.org/10.3390/math11244870 - 5 Dec 2023
Viewed by 999
Abstract
In this study, considering the delays for a susceptible individual becoming an alcoholic and the relapse of a recovered individual back into being an alcoholic, we formulate an epidemic model for alcoholism with distributed delays and relapse. The basic reproduction number R0 [...] Read more.
In this study, considering the delays for a susceptible individual becoming an alcoholic and the relapse of a recovered individual back into being an alcoholic, we formulate an epidemic model for alcoholism with distributed delays and relapse. The basic reproduction number R0 is calculated, and the threshold property of R0 is established. By analyzing the characteristic equation, we demonstrate the local asymptotic stability of the different equilibria under various conditions: when R0<1, the alcoholism-free equilibrium is locally asymptotically stable; when R0>1, the alcoholism equilibrium exists and is locally asymptotically stable. Furthermore, we demonstrate the global asymptotic stability at each equilibrium using a suitable Lyapunov function. Specifically, when R0<1, the alcoholism-free equilibrium is globally asymptotically stable; when R0>1, the alcoholism equilibrium is globally asymptotically stable. The sensitivity analysis of R0 shows that reducing exposure is more effective than treatment in controlling alcoholism. Interestingly, we found that extending the latency delay h1 and relapse delay h2 also effectively contribute to the control of the spread of alcoholism. Numerical simulations are also provided to support our theoretical results. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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11 pages, 4757 KiB  
Article
Analysis of Excitement Caused by Colored Noise in a Thermokinetic Model
by Lev Ryashko
Mathematics 2023, 11(22), 4676; https://doi.org/10.3390/math11224676 - 17 Nov 2023
Cited by 1 | Viewed by 624
Abstract
In this paper, a thermokinetic model forced by colored noise is studied. We analyze the mechanisms of stochastic excitement of equilibrium modes under variation of correlation time and noise intensity. It is shown that the phenomenon of colored-noise-induced excitement is accompanied by stochastic [...] Read more.
In this paper, a thermokinetic model forced by colored noise is studied. We analyze the mechanisms of stochastic excitement of equilibrium modes under variation of correlation time and noise intensity. It is shown that the phenomenon of colored-noise-induced excitement is accompanied by stochastic P-bifurcations. The region of the correlation parameter in which resonance occurs is localized. To study the phenomenon of colored-noise-induced excitement, we develop the probabilistic analysis based on the confidence domains method. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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