Infinite Dynamical System and Differential Equations

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

Deadline for manuscript submissions: 26 September 2024 | Viewed by 1589

Special Issue Editors


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Guest Editor
School of Science, Jiangnan University, Wuxi, China
Interests: infinite dynamical system; stability analysis in nonlinear systems; mathematical biology; infectious diseases

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modelling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Infinite dimensional dynamical systems and differential equations are important branches of mathematical research that have wide applications in many disciplines. Interdisciplinary research has become an inevitable trend in modern scientific research. Infinite dimensional dynamical systems and differential equations have become an indispensable bridge and link for interdisciplinary research, providing strong mathematical theoretical support and analytical methods for many fields such as economics, medicine, ecology, epidemiology, machine learning, artificial intelligence, etc.

The purpose of this Special Issue is to allow scientists and researchers to showcase their latest theories, research methods, and application achievements in infinite dynamical systems and differential equations, as well as in interdisciplinary research, for example, revolving around the existence, uniqueness, stability of solutions to various differential equations, optimal control theory, and the application of infinite dynamical systems in disciplines such as biomedicine, epidemiology, and population dynamics.

Dr. Cheng-Cheng Zhu
Prof. Dr. Hari Mohan Srivastava
Guest Editors

Manuscript Submission Information

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Keywords

  • infinite dynamical systems
  • global attractor
  • ODEs
  • PDEs
  • DDEs
  • operator semigroup theory
  • mathematical biology
  • population dynamics
  • mathematical epidemiology
  • nonlinear dynamical systems
  • non-autonomous systems
  • stability analysis
  • threshold dynamics
  • persistence theory
  • bifurcations and chaos
  • infectious diseases
  • optimal control theory
  • Stieltjes differential equations

Published Papers (2 papers)

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Research

16 pages, 301 KiB  
Article
On Using Relative Information to Estimate Traits in a Darwinian Evolution Population Dynamics
by Eddy Kwessi
Axioms 2024, 13(6), 406; https://doi.org/10.3390/axioms13060406 (registering DOI) - 16 Jun 2024
Viewed by 111
Abstract
Since its inception, evolution theory has garnered much attention from the scientific community for a good reason: it theorizes how various living organisms came to be and what changes are to be expected in a certain environment. While many models of evolution have [...] Read more.
Since its inception, evolution theory has garnered much attention from the scientific community for a good reason: it theorizes how various living organisms came to be and what changes are to be expected in a certain environment. While many models of evolution have been proposed to track changes in species’ traits, not much has been said about how to calculate or estimate these traits. In this paper, using information theory, we propose an estimation method for trait parameters in a Darwinian evolution model for species with one or multiple traits. We propose estimating parameters by minimizing the relative information in a Darwinian evolution population model using either a classical gradient ascent or a stochastic gradient ascent. The proposed procedure is shown to be possible in a supervised or unsupervised learning environment, similarly to what occurs with Boltzmann machines. Simulations are provided to illustrate the method. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
15 pages, 581 KiB  
Article
Approximate and Parametric Solutions to SIR Epidemic Model
by Lazhar Bougoffa, Smail Bougouffa and Ammar Khanfer
Axioms 2024, 13(3), 201; https://doi.org/10.3390/axioms13030201 - 16 Mar 2024
Viewed by 1076
Abstract
This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay [...] Read more.
This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robustness of the proposed approach, a numerical exploration is conducted, considering a diverse range of experimental parameters. This numerical analysis provides valuable insights into the sensitivity and responsiveness of the SIR epidemic model under varying conditions, contributing to the broader understanding of infectious disease dynamics. The interplay between theoretical formulation and numerical exploration establishes a comprehensive framework for studying the SIR model, with implications for refining our ability to predict and manage the spread of infectious diseases. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
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