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Axioms
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Mathematical Modeling, Simulations and Applications
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Mathematical Modeling, Simulations and Applications

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

Deadline for manuscript submissions: 28 May 2025 | Viewed by 3983

Special Issue Editors

Dr. Jun Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
Interests: biomathematic model; multi-scale geometry theory; bifurcation theory
Dr. Liang Zhang

E-Mail Website
Guest Editor
College of Science, Northwest A&F University, Yangling 712100, China
Interests: differential equations; biomathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, titled "Mathematical Modeling, Simulations and Applications", aims to provide a platform for exchanging academic research achievements, sharing innovative ideas, and advancing scientific progress. We welcome original research papers, review articles, and methodological contributions related to mathematical modeling, simulation, and applications.

This Special Issue covers, but is not limited to, the following topics:

  • Mathematical modeling: research including mathematical modeling methods and techniques in engineering, physics, biology, social science, and environmental science.
  • Numerical simulation and computation: research involving numerical methods, computational algorithms, high-performance computing, parallel computing, optimization techniques, and more.
  • Applied mathematics: applying mathematical theories and methods to solve real-world problems in various fields, such as engineering, science, medicine, finance, and economics.
  • Mathematics in science and engineering: research on the application of mathematics in fields such as physics, chemistry, biology, medicine, and engineering.
  • Mathematical modeling and simulation software development: the development and application of mathematical modeling and simulation software to support scientific research and engineering practice.

This Special Issue aims to promote interdisciplinary collaboration among mathematicians, applied mathematicians, and scientists from other fields, fostering idea exchange and advancing applied mathematics as a discipline. We look forward to receiving your high-quality submissions and believe that your research will make significant contributions to the development of mathematical modeling, simulation, and applications.

Best wishes

Dr. Jun Li
Dr. Liang Zhang
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. 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

  • mathematical modeling
  • simulation
  • applications
  • numerical methods
  • computational algorithms
  • mathematical applications
  • interdisciplinary collaboration
  • mathematical software development
  • engineering applications
  • scientific research
  • biomedical applications
  • environmental science
  • physics applications
  • social sciences
  • economics applications

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

Published Papers (5 papers)

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Research

24 pages, 2849 KiB  
Article
Optimization Decisions with Bounded Rationality in Customer-Intensive Services Under Gumbel Distributions
by Gang Fu, Minghui Jiang and Wentao Zhan
Axioms 2025, 14(4), 309; https://doi.org/10.3390/axioms14040309 - 17 Apr 2025
Viewed by 296
Abstract
Customers’ bounded rationality significantly influences the effectiveness of advertising and related decision-making in customer-intensive services. This paper, based on the M/M/1 queuing model and incorporating the characteristics of customers’ bounded rationality, conducts an optimization analysis of the decision-making of customer-intensive service providers. In [...] Read more.
Customers’ bounded rationality significantly influences the effectiveness of advertising and related decision-making in customer-intensive services. This paper, based on the M/M/1 queuing model and incorporating the characteristics of customers’ bounded rationality, conducts an optimization analysis of the decision-making of customer-intensive service providers. In this optimization process, we use the Gumbel distribution to model the random noise in customers’ bounded rationality, where the scale parameter characterizes the degree of bounded rationality, and customers’ choices follow a multinomial logit (MNL) choice model. We adopt the symmetric Nash equilibrium to prove the uniqueness of equilibrium in the duopoly market. Furthermore, we derive the optimal service rate and corresponding advertising expenditure levels for both monopoly and duopoly markets through optimization analysis. Our findings indicate that, regardless of market structure, an increase in the scale parameter of the Gumbel distribution, which captures customers’ bounded rationality, leads service providers to adopt a lower service rate to attract customers and reduce advertising expenditures. Notably, this strategy paradoxically results in higher profits for service providers. Additionally, we mathematically prove that, in both monopoly and duopoly markets, the proportion of customers choosing to enter the system follows a unimodal function of the service rate, and a unique and stable Nash equilibrium exists. Furthermore, we find that in the duopoly market, service providers, as a competitive strategy, set a lower service rate compared to the monopoly market. However, in the duopoly market, the proportion of customers attracted by each service provider is lower than in the monopoly market. We also confirmed the results through numerical simulation analysis. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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17 pages, 725 KiB  
Article
Polar Code BP Decoding Optimization for Green 6G Satellite Communication: A Geometry Perspective
by Chuanji Zhu, Yuanzhi He and Zheng Dou
Axioms 2025, 14(3), 174; https://doi.org/10.3390/axioms14030174 - 27 Feb 2025
Viewed by 375
Abstract
The rapid evolution of mega-constellation networks and 6G satellite communication systems has ushered in an era of ubiquitous connectivity, yet their sustainability is threatened by the energy-computation dilemma inherent in high-throughput data transmission. Polar codes, as a coding scheme capable of achieving Shannon’s [...] Read more.
The rapid evolution of mega-constellation networks and 6G satellite communication systems has ushered in an era of ubiquitous connectivity, yet their sustainability is threatened by the energy-computation dilemma inherent in high-throughput data transmission. Polar codes, as a coding scheme capable of achieving Shannon’s limit, have emerged as one of the key candidate coding technologies for 6G networks. Despite the high parallelism and excellent performance of their Belief Propagation (BP) decoding algorithm, its drawbacks of numerous iterations and slow convergence can lead to higher energy consumption, impacting system energy efficiency and sustainability. Therefore, research on efficient early termination algorithms has become an important direction in polar code research. In this paper, based on information geometry theory, we propose a novel geometric framework for BP decoding of polar codes and design two early termination algorithms under this framework: an early termination algorithm based on Riemannian distance and an early termination algorithm based on divergence. These algorithms improve convergence speed by geometrically analyzing the changes in soft information during the BP decoding process. Simulation results indicate that, when Eb/N0 is between 1.5 dB and 2.5 dB, compared to three classical early termination algorithms, the two early termination algorithms proposed in this paper reduce the number of iterations by 4.7–11% and 8.8–15.9%, respectively. Crucially, while this work is motivated by the unique demands of satellite networks, the geometric characterization of polar code BP decoding transcends specific applications. The proposed framework is inherently adaptable to any communication system requiring energy-efficient channel coding, including 6G terrestrial networks, Internet of Things (IoT) edge devices, and unmanned aerial vehicle (UAV) swarms, thereby bridging theoretical coding advances with real-world scalability challenges. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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18 pages, 402 KiB  
Article
Shock Model of K/N: G Repairable Retrial System Based on Discrete PH Repair Time
by Xiaoyun Yu, Linmin Hu and Zebin Hu
Axioms 2024, 13(12), 814; https://doi.org/10.3390/axioms13120814 - 21 Nov 2024
Viewed by 629
Abstract
A discrete time modeling method is employed in this paper to analyze and evaluate the reliability of a discrete time K/N: G repairable retrial system with Bernoulli shocks and two-stage repair. Lifetime and shocks are two factors that lead to [...] Read more.
A discrete time modeling method is employed in this paper to analyze and evaluate the reliability of a discrete time K/N: G repairable retrial system with Bernoulli shocks and two-stage repair. Lifetime and shocks are two factors that lead to component failure, and both of them can lead to the simultaneous failure of multiple components. When the repairman is busy, the newly failed component enters retrial orbit and retries in accordance with the first-in-first-out (FIFO) rule to obtain the repair. The repairman provides two-stage repair for failed components, all of which require basic repair and some of which require optional repair. The discrete PH distribution controls the repair times for two stages. Based on discrete time stochastic model properties, priority rules are defined when multiple events occur simultaneously. The state transition probability matrix and state set analysis are used to evaluate the system performance indexes. Numerical experiments are used to illustrate the main performance indexes of the developed discrete time model, and the impact of each parameter variation on the system indexes is examined. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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24 pages, 532 KiB  
Article
A Fast and Accurate Numerical Method for Solving Nonlinear Fourth-Order Boundary Value Problems in the Beam Theory
by Mohammad Ali Mehrpouya, Rezvan Salehi and Patricia J. Y. Wong
Axioms 2024, 13(11), 757; https://doi.org/10.3390/axioms13110757 - 31 Oct 2024
Cited by 1 | Viewed by 986
Abstract
In this paper, an efficient computational discretization approach is investigated for nonlinear fourth-order boundary value problems using beam theory. We specifically deal with nonlinear models described by fourth-order boundary value problems. The proposed method is applied on three different types of problems, i.e., [...] Read more.
In this paper, an efficient computational discretization approach is investigated for nonlinear fourth-order boundary value problems using beam theory. We specifically deal with nonlinear models described by fourth-order boundary value problems. The proposed method is applied on three different types of problems, i.e., the problem when an elastic bearing is non-zero (Case I), the problem under homogeneous boundary conditions of the unknown function and its second derivative (Case II), and the problem with integral boundary conditions (Case III). Moreover, the convergence analysis of the proposed method is provided. Finally, illustrative examples are included to demonstrate the applicability and validity of the technique and the comparison is made with the existing methods to show the efficiency and accuracy of the proposed method. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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25 pages, 2125 KiB  
Article
Dynamic Analysis and Optimal Control of a Fractional Order Fishery Model with Refuge and Protected Area
by Wenjun Gao, Xiu Jia and Ruiqing Shi
Axioms 2024, 13(9), 642; https://doi.org/10.3390/axioms13090642 - 19 Sep 2024
Viewed by 925
Abstract
In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to [...] Read more.
In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin’s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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