Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\)
Volume 11, Issue 4, pp 477--485
http://dx.doi.org/10.22436/jnsa.011.04.04
Publication Date: March 16, 2018
Submission Date: February 04, 2017
Revision Date: November 25, 2017
Accteptance Date: January 11, 0018
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Authors
Taixiang Sun
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China.
Hongjian Xi
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China.
Guangwang Su
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China.
Bin Qin
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, China.
Abstract
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 \(2m\).
Share and Cite
ISRP Style
Taixiang Sun, Hongjian Xi, Guangwang Su, Bin Qin, 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 Applications, 11 (2018), no. 4, 477--485
AMA Style
Sun Taixiang, Xi Hongjian, Su Guangwang, Qin Bin, Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\). J. Nonlinear Sci. Appl. (2018); 11(4):477--485
Chicago/Turabian Style
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 Applications, 11, no. 4 (2018): 477--485
Keywords
- Fuzzy max-type difference equation
- positive solution
- eventual periodicity
MSC
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