Periodic Solution for a Max-Type Fuzzy Difference Equation
The paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/3094391 |
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| _version_ | 1832566444302270464 |
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| author | Changyou Wang Jiahui Li |
| author_facet | Changyou Wang Jiahui Li |
| author_sort | Changyou Wang |
| collection | DOAJ |
| description | The paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive fuzzy numbers. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. In addition, the boundedness and persistence of solutions for the fuzzy difference equation is proved. Finally, the results of this paper are simulated and verified by using MATLAB 2016 software package. |
| format | Article |
| id | doaj-art-dc37ccc78e6942b39441253f1162528a |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-dc37ccc78e6942b39441253f1162528a2025-02-03T01:04:08ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/30943913094391Periodic Solution for a Max-Type Fuzzy Difference EquationChangyou Wang0Jiahui Li1College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, ChinaCollege of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, ChinaThe paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive fuzzy numbers. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. In addition, the boundedness and persistence of solutions for the fuzzy difference equation is proved. Finally, the results of this paper are simulated and verified by using MATLAB 2016 software package.http://dx.doi.org/10.1155/2020/3094391 |
| spellingShingle | Changyou Wang Jiahui Li Periodic Solution for a Max-Type Fuzzy Difference Equation Journal of Mathematics |
| title | Periodic Solution for a Max-Type Fuzzy Difference Equation |
| title_full | Periodic Solution for a Max-Type Fuzzy Difference Equation |
| title_fullStr | Periodic Solution for a Max-Type Fuzzy Difference Equation |
| title_full_unstemmed | Periodic Solution for a Max-Type Fuzzy Difference Equation |
| title_short | Periodic Solution for a Max-Type Fuzzy Difference Equation |
| title_sort | periodic solution for a max type fuzzy difference equation |
| url | http://dx.doi.org/10.1155/2020/3094391 |
| work_keys_str_mv | AT changyouwang periodicsolutionforamaxtypefuzzydifferenceequation AT jiahuili periodicsolutionforamaxtypefuzzydifferenceequation |