ASYMPTOTIC FEATURE OF DISCRETE SECOND-ORDER FUZZY DIFFERENCE EQUATION WITH QUADRATIC TERM

Qianhong Zhang; Fei Jin; Zhongni Zhang; Bairong Pan

doi:10.11948/20230342

2025 Volume 15 Issue 2

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Qianhong Zhang, Fei Jin, Zhongni Zhang, Bairong Pan. ASYMPTOTIC FEATURE OF DISCRETE SECOND-ORDER FUZZY DIFFERENCE EQUATION WITH QUADRATIC TERM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 640-656. doi: 10.11948/20230342

Citation:

Qianhong Zhang, Fei Jin, Zhongni Zhang, Bairong Pan. ASYMPTOTIC FEATURE OF DISCRETE SECOND-ORDER FUZZY DIFFERENCE EQUATION WITH QUADRATIC TERM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 640-656. doi: 10.11948/20230342

ASYMPTOTIC FEATURE OF DISCRETE SECOND-ORDER FUZZY DIFFERENCE EQUATION WITH QUADRATIC TERM

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Huayan Road, 550025 Guiyang, China
2.
Guizhou Key Laboratory of Big Data Statistics and Analysis, Guizhou University of Finance and Economics, Huayan Road, 550025 Guiyang, China

Author Bio: Email: 577661973@qq.com(F. Jin); Email: 981092675@qq.com(Z. Zhang); Email: 1193602723@qq.com(B. Pan)
Corresponding author: Email: zqianhong68@163.com(Q. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (12461038), Guizhou Scientific and Technological Platform Talents (GCC[2022]020-1), Scientific Research Foundation of Guizhou Provincial Department of Science and Technology ([2022]021, [2022]026), and Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province (No. 2023013)

Abstract

Abstract

This article explores the asymptotic feature of a discrete second-order fractal FDE (fuzzy difference equation) with quadratic term. Specifically, applying a generalization of division (g-division) of two fuzzy numbers, we obtain dynamical features including the boundedness, persistence, and global behavior of a positive fuzzy solution of the following model

$ x_{n+1}=A+\frac{Bx_{n}^2}{x_{n-1}^2}, \ \ n\in N^+, $

where the parameters $A, B\in \Re_f^+$(positive fuzzy number) and the initial values $x_0, x_{-1}\in \Re_f^+$. Finally, two numerical examples are provided to reveal the validity of our findings.
- g-division /
- fractal FDE /
- persistence /
- boundedness /
- global asymptotic feature
MSC: 39A10

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References

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