DYNAMIC BEHAVIOR OF A SEVEN-ORDER FUZZY DIFFERENCE EQUATION

Lili Jia; Xiaojuan Zhao; Changyou Wang; Qiyu Wang

doi:10.11948/20220340

2023 Volume 13 Issue 1

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Lili Jia, Xiaojuan Zhao, Changyou Wang, Qiyu Wang. DYNAMIC BEHAVIOR OF A SEVEN-ORDER FUZZY DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 486-501. doi: 10.11948/20220340

Citation:

Lili Jia, Xiaojuan Zhao, Changyou Wang, Qiyu Wang. DYNAMIC BEHAVIOR OF A SEVEN-ORDER FUZZY DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 486-501. doi: 10.11948/20220340

DYNAMIC BEHAVIOR OF A SEVEN-ORDER FUZZY DIFFERENCE EQUATION

1.
Dianchi College of Yunnan University, Kunming 650228, China
2.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China

Corresponding author: Email: wangchangyou417@163.com(C. Wang)

Abstract

Abstract

In this paper, we explore the qualitative features of a seven-order fuzzy difference equation
$x_{n+1}=\frac{A x_{n-1}}{B+C x_{n-2}^{p} x_{n-4}^{q} x_{n-6}^{r}}, n=0, 1, 2, \cdots, $
here the parameters $A, B, C$ $\in$ $R$$_f^+$, $p, q, r$ $\in$ $R$$^+$ and the initial values $x$$_{-6}$, $\cdots$, $x$$_{-1}$, $x$$_{0}$$\in$ $R$$_f^+$. Utilizing the fuzzy sets theory, linearization method, mathematical induction and inequality technique, we obtain some sufficient condition on the qualitative features including the boundedness of the positive solution of the equation and the stability and instability of the equilibrium point of the equation. Moreover, two simulation examples are presented to verify the effectiveness of our proposed results.
- Fuzzy difference equation /
- equilibrium point /
- boundedness /
- stability /
- unstability
MSC: 39A10

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References

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