DYNAMICS OF A HIGH-ORDER NONLINEAR FUZZY DIFFERENCE EQUATION

Changyou Wang; Jiahui Li; Lili Jia

doi:10.11948/20200050

2021 Volume 11 Issue 1

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Changyou Wang, Jiahui Li, Lili Jia. DYNAMICS OF A HIGH-ORDER NONLINEAR FUZZY DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 404-421. doi: 10.11948/20200050

Citation:

Changyou Wang, Jiahui Li, Lili Jia. DYNAMICS OF A HIGH-ORDER NONLINEAR FUZZY DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 404-421. doi: 10.11948/20200050

DYNAMICS OF A HIGH-ORDER NONLINEAR FUZZY DIFFERENCE EQUATION

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

Corresponding authors: Email addresses:wangchangyou417@163.com (C. Wang); Email addresses: jialilidianchi1982@163.com (L. Jia)
Fund Project: This work is supported by the Scientific Research Fund of Chengdu University of Information Technology (No. KYTZ201820) of China, the Sichuan Science and Technology Program (No. 2018JY0480) of China, and the scientific research fund of the Yunnan Provincial Education Department under grant number (No. 2018JS737) of China

Abstract

Abstract

This paper is concerned with the following high-order nonlinear fuzzy difference system

$ {x_{n + 1}} = \frac{{A{\kern 1pt} {x_{n - m}}}}{{B + C{\kern 1pt} \prod\limits_{i = 0}^m {{x_{n - i}}} }}, {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} n = 0, 1, 2, \cdots , $

where $ {x_n} $ is a sequence of positive fuzzy numbers, the parameters and the initial conditions $ {x_{ - m}}, \;{x_{ - m + 1}}, \; \cdots , {x_0} $ are positive fuzzy numbers, $ m $ is non-negative integer. More accurately, our main purpose is to study the existence and uniqueness of the positive solutions, the boundedness of the positive solutions, the instability, local asymptotic stability and global asymptotic stability of the equilibrium points for the above equation by using the iteration method, the inequality skills, the mathematical induction, and the monotone boundedness theorem. Moreover, some numerical examples to the difference system are given to verify our theoretical results.
- Fuzzy difference equation /
- boundedness /
- equilibrium point /
- asymptotic behavior
MSC: 39A10

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