Geodesic
Dynamics of the fuzzy difference equation $z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}$ :
Sun, Taixiang 1   ; Xi, Hongjian 1   ; Su, Guangwang 1   ; Qin, Bin 1
1 Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 477-485 Cet article a éte moissonné depuis la source International Scientific Research Publications

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In this paper, we study the eventual periodicity of the following fuzzy max-type difference equation

$z_n=\max\{\frac{1}{z_{n-m}},\frac{\alpha_n}{z_{n-r}}\},\ \ n=0,1,\ldots,$

where $\{\alpha_n\}_{n\geq 0}$ is a periodic sequence of positive fuzzy numbers and the initial values $z_{-d},z_{-d+1},\ldots,z_{-1}$ are positive fuzzy numbers with $d=\max\{m,r\}$. We show that if $\max(\mbox{supp}\ \alpha_n)1$, then every positive solution of this equation is eventually periodic with period $2m$.

DOI : 10.22436/jnsa.011.04.04
Classification : 39A10, 39A11
Keywords: Fuzzy max-type difference equation, positive solution, eventual periodicity

Sun, Taixiang   1   ; Xi, Hongjian   1   ; Su, Guangwang   1   ; Qin, Bin   1

1 Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China 
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     journal = {Journal of nonlinear sciences and its applications},
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Sun, Taixiang ; Xi, Hongjian ; Su, Guangwang ; Qin, Bin . Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\). Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 477-485. doi: 10.22436/jnsa.011.04.04

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