Application of Mathematical Method and Models in Dynamic System, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 1256

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Department of Mathematics, Politehnica University of Timişoara, Piata Victoriei No. 2, 300006 Timişoara, Romania
Interests: Hamilton-Poisson systems; nonlinear dynamical systems; bifurcations; mathematical models
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Special Issue Information

Dear Colleague,

The most observed phenomena in scientific investigation and in everyday life are dynamic phenomena. The list of these phenomena is rich, including life systems, physical systems, or social systems, encompassing population growth, ecological decay, epidemics of disease, the motion of a system of particles, the behavior of an economic structure, etc. Some such phenomena are easy to understand, but others require a proper mathematical model, usually represented in terms of either differential or difference equations. This includes continuous-time dynamical systems, piecewise dynamical systems, discrete-time dynamical systems, time-delay dynamical systems, fractional order dynamical systems, and fast–slow dynamical systems, among others.

The aim of this Special Issue is to establish new mathematical models and study their behavior and properties, or those of existing dynamical systems using known or new methods.

Dr. Cristian Lazureanu
Guest Editor

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Keywords

  • mathematical models
  • dynamic systems
  • bifurcations
  • chaotic behavior
  • controllability
  • integrability
  • numerical methods
  • numerical simulations
  • stability

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Related Special Issue

Published Papers (2 papers)

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Research

31 pages, 7527 KiB  
Article
A Multi-Age Multi-Group Epidemiological Model and Its Validation on the COVID-19 Epidemic in Italy: SEIHRDV
by Luca Dede’, Nicola Parolini, Alfio Quarteroni, Giulia Villani and Giovanni Ziarelli
Mathematics 2025, 13(5), 788; https://doi.org/10.3390/math13050788 - 27 Feb 2025
Viewed by 371
Abstract
We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, validated using data from Italy starting in September 2020. SEIHRDV includes the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased [...] Read more.
We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, validated using data from Italy starting in September 2020. SEIHRDV includes the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased (D), and Vaccinated (V). The model is age-stratified, with the population divided into 15 age groups, and it considers seven different contexts of exposure to infection (family, home, school, work, transport, leisure, and other contexts), which impact the transmission mechanism. The primary goal of this work is to provide a valuable tool for analyzing the spread of the epidemic in Italy during 2020 and 2021, supporting the country’s decision making processes. By leveraging the SEIHRDV model, we analyzed epidemic trends, assessed the efficacy of non-pharmaceutical interventions, and evaluated vaccination strategies, including the introduction of the Green Pass, a containment measure implemented in Italy in 2021. The model proved instrumental in conducting comprehensive what-if studies and scenario analyses tailored to Italy and its regions. Furthermore, SEIHRDV facilitated accurate forecasting of the future potential trajectory of the epidemic, providing critical insights for improved public health strategies and informed decision making for authorities. Full article
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24 pages, 769 KiB  
Article
Quantitative Controllability Metric for Disturbance Rejection in Linear Unstable Systems
by Haemin Lee and Jinseong Park
Mathematics 2025, 13(1), 6; https://doi.org/10.3390/math13010006 - 24 Dec 2024
Viewed by 578
Abstract
This paper introduces a novel Gramian-based quantitative metric to evaluate the disturbance rejection capabilities of linear unstable systems. The proposed metric addresses key limitations of the previously introduced degree of disturbance rejection (DoDR) metrics, including their dependency on the final time and numerical [...] Read more.
This paper introduces a novel Gramian-based quantitative metric to evaluate the disturbance rejection capabilities of linear unstable systems. The proposed metric addresses key limitations of the previously introduced degree of disturbance rejection (DoDR) metrics, including their dependency on the final time and numerical problems arising from differential equation computations. Specifically, this study defines the steady-state solution of the DoDR metric, which avoids numerical issues by relying only on solving four algebraic equations, even when the Gramian matrices diverge. This study further strengthens its contributions by providing rigorous mathematical proofs supporting the proposed method, ensuring a strong theoretical foundation. The derived results demonstrate that the proposed metric represents the sum of the steady-state input energies required to reject the disturbances in the asymptotically stable and anti-stable subsystems. Numerical examples demonstrated that the proposed metric maintained the physical meaning of the original DoDR while offering practical computational advantages. This study represents a significant step toward the efficient and reliable assessment of disturbance rejection capabilities in unstable systems. Full article
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