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Axioms
Special Issues
Recent Advances in Applied Mathematics and Artificial Intelligence
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Recent Advances in Applied Mathematics and Artificial Intelligence

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (29 January 2025) | Viewed by 5496

Special Issue Editors

Prof. Dr. Ruizhi Yang

E-Mail Website
Guest Editor
College of Science, Northeast Forestry University, Harbin 150040, China
Interests: functional differential equations (bifurcation theory and numerical analysis); reaction diffusion equation (bifurcation theory of and its application); mathematical biology (predator-prey model)
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yining Xie

E-Mail Website
Guest Editor
School of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Interests: applied mathematics and artificial intelligence; intelligent control; image processing; speech recognition

Special Issue Information

Dear Colleagues,

The journal Axioms is an international, open access journal which provides an advanced forum for studies related to mathematics, mathematical logic and mathematical physics. This Special Issue focuses on Applied Mathematics and Artificial Intelligence, since they have a wide range of applications in real life, such as engineering, physics, medicine, and economics. The aim of this Special Issue is to seek advancements in the discourse on all aspects of Applied Mathematics and Artificial Intelligence. This Special Issue invites papers on innovative proposals of the theory and application of Applied Mathematics and Artificial Intelligence. 

Dr. Ruizhi Yang
Prof. Dr. Yining Xie
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 model
  • dynamic system
  • local and global dynamics
  • machine learning
  • learning algorithms
  • pattern recognition
  • data filtering and transformation
  • feature extraction and analysis
  • deep learning algorithm

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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

17 pages, 385 KiB  
Article
pth Moment Exponential Synchronization of Fuzzy Stochastic Cellular Neural Networks with Discrete and Infinite Delays
by Keyu Xu, Ming Liu and Xiaofeng Xu
Axioms 2025, 14(2), 142; https://doi.org/10.3390/axioms14020142 - 19 Feb 2025
Viewed by 184
Abstract
In this paper, we consider the pth moment exponential synchronization (PMES) of fuzzy stochastic cellular neural networks (FSCNNs) with discrete and infinite delays. In order to achieve pth-moment exponential synchronization of FSCNNs with discrete and infinite delays, we design an appropriate [...] Read more.
In this paper, we consider the pth moment exponential synchronization (PMES) of fuzzy stochastic cellular neural networks (FSCNNs) with discrete and infinite delays. In order to achieve pth-moment exponential synchronization of FSCNNs with discrete and infinite delays, we design an appropriate feedback controller. Using the Lyapunov function method and theories of infinite delayed systems, we obtain some sufficient conditions to ensure the pth-moment exponential synchronization of the system. Finally, to verify the effectiveness of our results, we provide a numerical simulation example. Our results extend the pth-moment exponential synchronization of FSCNNs from finite delays systems to infinite delays systems. Full article
(This article belongs to the Special Issue Recent Advances in Applied Mathematics and Artificial Intelligence)
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23 pages, 1129 KiB  
Article
A Computational Approach to the Perimeter-Area Inequality in a Triangle
by Tomás Recio, Carlos Ueno and María Pilar Vélez
Axioms 2025, 14(1), 40; https://doi.org/10.3390/axioms14010040 - 5 Jan 2025
Viewed by 869
Abstract
This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind these tools, this study analyzes a geometric construction involving a triangle [...] Read more.
This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind these tools, this study analyzes a geometric construction involving a triangle with arbitrary side lengths and area, investigating the automated derivation of the relationship between the area and perimeter of a triangle, and showing that only equilateral triangles satisfy the exact perimeter-area equality. The main contribution of this work is to describe the challenges, and potential ways to approach their solutions, still posed by the use of such automated, symbolic computation, methods in dynamic geometry, in particular concerning the discovery of loci of points that satisfy specific geometric conditions, suggesting relevant improvements for the future development of these symbolic AI-based educational tools in geometry. Full article
(This article belongs to the Special Issue Recent Advances in Applied Mathematics and Artificial Intelligence)
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Graphical abstract

22 pages, 533 KiB  
Article
Fixed Time Synchronization of Stochastic Takagi–Sugeno Fuzzy Recurrent Neural Networks with Distributed Delay under Feedback and Adaptive Controls
by Yiran Niu, Xiaofeng Xu and Ming Liu
Axioms 2024, 13(6), 391; https://doi.org/10.3390/axioms13060391 - 11 Jun 2024
Cited by 1 | Viewed by 799
Abstract
In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to synchronize the networks, we design two kinds of controllers: a [...] Read more.
In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to synchronize the networks, we design two kinds of controllers: a feedback controller and an adaptive controller. Then, we obtain the synchronization criteria in a fixed time by combining the Lyapunov method and the related inequality theory of the stochastic differential equation and calculate the stabilization time for the STSFRNNS. In addition, to verify the authenticity of the theoretical results, we use MATLABR2023A to carry out numerical simulation. Full article
(This article belongs to the Special Issue Recent Advances in Applied Mathematics and Artificial Intelligence)
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23 pages, 1490 KiB  
Article
Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response
by Yuan Xue, Jinli Xu and Yuting Ding
Axioms 2023, 12(12), 1085; https://doi.org/10.3390/axioms12121085 - 27 Nov 2023
Viewed by 1245
Abstract
In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we [...] Read more.
In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results. Full article
(This article belongs to the Special Issue Recent Advances in Applied Mathematics and Artificial Intelligence)
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17 pages, 701 KiB  
Article
Dynamics of a Prey–Predator Model with Group Defense for Prey, Cooperative Hunting for Predator, and Lévy Jump
by Hengfei Chen, Ming Liu and Xiaofeng Xu
Axioms 2023, 12(9), 878; https://doi.org/10.3390/axioms12090878 - 14 Sep 2023
Cited by 1 | Viewed by 1436
Abstract
A stochastic predator–prey system with group cooperative behavior, white noise, and Lévy noise is considered. In group cooperation, we introduce the Holling IV interaction term to reflect group defense of prey, and cooperative hunting to reflect group attack of predator. Firstly, it is [...] Read more.
A stochastic predator–prey system with group cooperative behavior, white noise, and Lévy noise is considered. In group cooperation, we introduce the Holling IV interaction term to reflect group defense of prey, and cooperative hunting to reflect group attack of predator. Firstly, it is proved that the system has a globally unique positive solution. Secondly, we obtain the conditions of persistence and extinction of the system in the sense of time average. Under the condition that the environment does not change dramatically, the intensity of cooperative hunting and group defense needs to meet certain conditions to make both predators and preys persist. In addition, considering the system without Lévy jump, it is proved that the system has a stationary distribution. Finally, the validity of the theoretical results is verified by numerical simulation. Full article
(This article belongs to the Special Issue Recent Advances in Applied Mathematics and Artificial Intelligence)
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