Eventual periodicity of the fuzzy max-difference equation \(x_{n} = \max \{ C, \frac{x_{n-m-k}}{x_{n-m}}\}\)

Advances in Difference Equations

article

Han, Caihong¹  Su, Guangwang¹  Li, Lue¹  Xia, Guoen³  Sun, Taixiang¹ 

[1] College of Information and Statistics, Guangxi University of Finance and Economics;Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing;College of Business Administration, Guangxi University of Finance and Economics

关键词: Fuzzy max-type difference equation;    Positive solution;    Eventual periodicity;   

DOI  :  10.1186/s13662-020-03136-4

学科分类：航空航天科学

来源: SpringerOpen

【 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

【 授权许可】

CC BY