Research Article
Open Access
Dynamical Behavior of a Second-Order Exponential-Type Fuzzy Difference Equation with Quadratic Term
1
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
* Corresponding Author:
Qianhong Zhang,
[email protected]
Volume 1, Issue 1
2025
Received: 16 August 2025
Accepted: 28 October 2025
Published: 28 November 2025
Article Information
Abstract
The paper discusses the dynamical characteristics of solutions to a model with quadratic term. More precisely, an exponential-type fuzzy difference equation is proposed as follows $$ a_{n+1}=\frac{D+Pe^{-a_n}}{T+a^2_{n-1}},\ \ n=0,1,\cdots ,$$ here $D, P, T$ and $a_0, a_{-1}$ belong to positive fuzzy numbers. This model can be used to characterize the diffusion modeling of a class of infectious diseases with uncertainty, such as the transmission prediction of dengue fever, monkeypox, and other infectious diseases. In addition, by highlighting the advantages of using Stefanini's the generalization of division of fuzzy number (it is also known as g-division) and constructing a Lyapunov function, we primarily obtain the dynamical characteristics of the model discussed above, such as convergence of single positive equilibrium and persistence, global asymptotical stability and boundedness of positive solutions. Furthermore, some numerical examples are provided to confirm the theoretical findings.
Graphical Abstract
Keywords
fuzzy difference equation
boundedness
global asymptotic behavior
g-Division
Data Availability Statement
Data will be made available on request.
Funding
This work was supported in part by the National Natural Science Foundation of China under Grant 12461038; in part by the Guizhou Scientific and Technological Platform Talents under Grant GCC[2022] 020-1; in part by the Scientific Research Foundation of Guizhou Provincial Department of Science and Technology under Grant [2022]021 and Grant [2022]026; in part by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province under Grant 2023013.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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Cited By (1)
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Xiong Xiao, Qianhong Zhang. Global asymptotic stability and qualitative analysis of fuzzy difference equations with composite exponential saturation and parabolic fuzzy parameters.
AIMS Mathematics, 2026 , 11 (6).
[CrossRef]
* Citation data provided by Crossref Cited-by.
Cite This Article
APA Style
Lin, K., & Zhang, Q. (2025). Dynamical Behavior of a Second-Order Exponential-Type Fuzzy Difference Equation with Quadratic Term. Journal of Mathematics and Interdisciplinary Applications, 1(1), 29–50. https://doi.org/10.62762/JMIA.2025.999827
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TY - JOUR
AU - Lin, Kexiang
AU - Zhang, Qianhong
PY - 2025
DA - 2025/11/28
TI - Dynamical Behavior of a Second-Order Exponential-Type Fuzzy Difference Equation with Quadratic Term
JO - Journal of Mathematics and Interdisciplinary Applications
T2 - Journal of Mathematics and Interdisciplinary Applications
JF - Journal of Mathematics and Interdisciplinary Applications
VL - 1
IS - 1
SP - 29
EP - 50
DO - 10.62762/JMIA.2025.999827
UR - https://www.icck.org/article/abs/JMIA.2025.999827
KW - fuzzy difference equation
KW - boundedness
KW - global asymptotic behavior
KW - g-Division
AB - The paper discusses the dynamical characteristics of solutions to a model with quadratic term. More precisely, an exponential-type fuzzy difference equation is proposed as follows $$ a_{n+1}=\frac{D+Pe^{-a_n}}{T+a^2_{n-1}},\ \ n=0,1,\cdots ,$$ here $D, P, T$ and $a_0, a_{-1}$ belong to positive fuzzy numbers. This model can be used to characterize the diffusion modeling of a class of infectious diseases with uncertainty, such as the transmission prediction of dengue fever, monkeypox, and other infectious diseases. In addition, by highlighting the advantages of using Stefanini's the generalization of division of fuzzy number (it is also known as g-division) and constructing a Lyapunov function, we primarily obtain the dynamical characteristics of the model discussed above, such as convergence of single positive equilibrium and persistence, global asymptotical stability and boundedness of positive solutions. Furthermore, some numerical examples are provided to confirm the theoretical findings.
SN - 3070-393X
PB - Institute of Central Computation and Knowledge
LA - English
ER -
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Compatible with LaTeX, BibTeX, and other reference managers
@article{Lin2025Dynamical,
author = {Kexiang Lin and Qianhong Zhang},
title = {Dynamical Behavior of a Second-Order Exponential-Type Fuzzy Difference Equation with Quadratic Term},
journal = {Journal of Mathematics and Interdisciplinary Applications},
year = {2025},
volume = {1},
number = {1},
pages = {29-50},
doi = {10.62762/JMIA.2025.999827},
url = {https://www.icck.org/article/abs/JMIA.2025.999827},
abstract = {The paper discusses the dynamical characteristics of solutions to a model with quadratic term. More precisely, an exponential-type fuzzy difference equation is proposed as follows \$\$ a\_{n+1}=\frac{D+Pe^{-a\_n}}{T+a^2\_{n-1}},\ \ n=0,1,\cdots ,\$\$ here \$D, P, T\$ and \$a\_0, a\_{-1}\$ belong to positive fuzzy numbers. This model can be used to characterize the diffusion modeling of a class of infectious diseases with uncertainty, such as the transmission prediction of dengue fever, monkeypox, and other infectious diseases. In addition, by highlighting the advantages of using Stefanini's the generalization of division of fuzzy number (it is also known as g-division) and constructing a Lyapunov function, we primarily obtain the dynamical characteristics of the model discussed above, such as convergence of single positive equilibrium and persistence, global asymptotical stability and boundedness of positive solutions. Furthermore, some numerical examples are provided to confirm the theoretical findings.},
keywords = {fuzzy difference equation, boundedness, global asymptotic behavior, g-Division},
issn = {3070-393X},
publisher = {Institute of Central Computation and Knowledge}
}
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Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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