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标题：Eventual periodicity of the fuzzy max-difference equation x n = max { C , x n − m − k x n − m } $x_{n} = \max \{ C, \frac{x_{n-m-k}}{x_{n-m}}\}$
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作者：Caihong Han ; Guangwang Su ; Lue Li 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-10
DOI：10.1186/s13662-020-03136-4
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the eventual periodicity of the fuzzy max-type difference equation $x_{n} =\max \{C , \frac{x_{n-m-k}}{x_{n-m} }\}, n\in \{0,1,\ldots \} $ , where m and k are positive integers, C and the initial values are positive fuzzy numbers. Let the support $\operatorname{supp} C=\overline{\{t : C(t) > 0\}}=[C_{1},C_{2}]$ of C. We show that: (1) if $C_{1}>1$ , then every positive solution of this equation equals C eventually; (2) there exists a positive fuzzy number C with $C_{1}=1$ such that this equation has a positive solution which is not eventually periodic; (3) if $C_{2}\leq 1$ , then this equation has a positive solution which is not eventually periodic; (4) if $C_{1}<1
关键词：Fuzzy max-type difference equation ; Positive solution ; Eventual periodicity