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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: 30 June 2024 | Viewed by 1965

Special Issue Editors

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

Published Papers (2 papers)

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Research

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 829
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
Viewed by 783
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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