Research Article
Open Access
Dynamic Behavior of a Population Model Based on Second-order Fuzzy Difference Equation
1
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2
School of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
* Corresponding Author:
Qianhong Zhang,
[email protected]
Volume 2, Issue 2
2026
Received: 07 April 2026
Accepted: 28 May 2026
Published: 06 June 2026
Article Information
Volume/Issue
Volume 2, Issue 2, 2026
Pages
112-124
Abstract
This article examines the dynamic behavior of a second-order fuzzy difference equation that models the quantitative changes in a specific biological population: $$ E_{n+1}=\frac{S}{C+E_n+E_{n-1}},\ n\in \mathbb{Z}\ and\ n\ge 0,$$ Here, parameter $S$ represents the carrying capacity of the environment, while $C$ signifies the minimum resources required for population survival. The initial values $E_0$, $E_{-1}$, and parameters $S$ , $C$ are all positive fuzzy numbers. By employing the generalized division (g-division) with respect to fuzzy numbers, we establish the existence, uniqueness, persistence, and boundedness of positive fuzzy solutions to the equation under specified conditions. Furthermore, we derive the local and global asymptotic stability of these fuzzy solutions. Finally, two examples are provided to substantiate the conclusions drawn.
Graphical Abstract
Keywords
fuzzy difference equation
persistence and boundedness
local and global behavior
g-division
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the Postgraduate Research Foundation of GUFE under Grant 2025BAZYSY213, and by the Guizhou Scientific and Technological Platform Talents under Grant GCC[2022]020-2.
Conflicts of Interest
The authors declare no conflicts of interest.
AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
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Cite This Article
APA Style
Xiao, X., & Zhang, Q. (2026). Dynamic Behavior of a Population Model Based on Second-order Fuzzy Difference Equation. Journal of Mathematics and Interdisciplinary Applications, 2(2), 112-124. https://doi.org/10.62762/JMIA.2026.547303
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TY - JOUR
AU - Xiao, Xiong
AU - Zhang, Qianhong
PY - 2026
DA - 2026/06/06
TI - Dynamic Behavior of a Population Model Based on Second-order Fuzzy Difference Equation
JO - Journal of Mathematics and Interdisciplinary Applications
T2 - Journal of Mathematics and Interdisciplinary Applications
JF - Journal of Mathematics and Interdisciplinary Applications
VL - 2
IS - 2
SP - 112
EP - 124
DO - 10.62762/JMIA.2026.547303
UR - https://www.icck.org/article/abs/JMIA.2026.547303
KW - fuzzy difference equation
KW - persistence and boundedness
KW - local and global behavior
KW - g-division
AB - This article examines the dynamic behavior of a second-order fuzzy difference equation that models the quantitative changes in a specific biological population: $$ E_{n+1}=\frac{S}{C+E_n+E_{n-1}},\ n\in \mathbb{Z}\ and\ n\ge 0,$$ Here, parameter $S$ represents the carrying capacity of the environment, while $C$ signifies the minimum resources required for population survival. The initial values $E_0$, $E_{-1}$, and parameters $S$ , $C$ are all positive fuzzy numbers. By employing the generalized division (g-division) with respect to fuzzy numbers, we establish the existence, uniqueness, persistence, and boundedness of positive fuzzy solutions to the equation under specified conditions. Furthermore, we derive the local and global asymptotic stability of these fuzzy solutions. Finally, two examples are provided to substantiate the conclusions drawn.
SN - 3070-393X
PB - Institute of Central Computation and Knowledge
LA - English
ER -
BibTeX Format
Compatible with LaTeX, BibTeX, and other reference managers
@article{Xiao2026Dynamic,
author = {Xiong Xiao and Qianhong Zhang},
title = {Dynamic Behavior of a Population Model Based on Second-order Fuzzy Difference Equation},
journal = {Journal of Mathematics and Interdisciplinary Applications},
year = {2026},
volume = {2},
number = {2},
pages = {112-124},
doi = {10.62762/JMIA.2026.547303},
url = {https://www.icck.org/article/abs/JMIA.2026.547303},
abstract = {This article examines the dynamic behavior of a second-order fuzzy difference equation that models the quantitative changes in a specific biological population: \$\$ E\_{n+1}=\frac{S}{C+E\_n+E\_{n-1}},\ n\in \mathbb{Z}\ and\ n\ge 0,\$\$ Here, parameter \$S\$ represents the carrying capacity of the environment, while \$C\$ signifies the minimum resources required for population survival. The initial values \$E\_0\$, \$E\_{-1}\$, and parameters \$S\$ , \$C\$ are all positive fuzzy numbers. By employing the generalized division (g-division) with respect to fuzzy numbers, we establish the existence, uniqueness, persistence, and boundedness of positive fuzzy solutions to the equation under specified conditions. Furthermore, we derive the local and global asymptotic stability of these fuzzy solutions. Finally, two examples are provided to substantiate the conclusions drawn.},
keywords = {fuzzy difference equation, persistence and boundedness, local and global behavior, g-division},
issn = {3070-393X},
publisher = {Institute of Central Computation and Knowledge}
}
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Copyright © 2026 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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