Periodicities of a System of Difference Equations
We study the periodicities of a system of difference equations xn+1=max1/xn,An/yn-k,yn+1=max1/yn,Bn/xn-k, where initial values (x-k,y-k),…,(x0,y0)∈(0,+∞)×(0,+∞). We show that if An,Bn∈(0,1) are two periodic sequences, then every solution of the above system is eventually periodic with period 2. If k...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/2095805 |
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| _version_ | 1832562833256087552 |
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| author | Weizhen Quan Miaoqiao Pan Xiaopei Li |
| author_facet | Weizhen Quan Miaoqiao Pan Xiaopei Li |
| author_sort | Weizhen Quan |
| collection | DOAJ |
| description | We study the periodicities of a system of difference equations xn+1=max1/xn,An/yn-k,yn+1=max1/yn,Bn/xn-k, where initial values (x-k,y-k),…,(x0,y0)∈(0,+∞)×(0,+∞). We show that if An,Bn∈(0,1) are two periodic sequences, then every solution of the above system is eventually periodic with period 2. If k is even, there must be one in xn and yn converges to period two solution. |
| format | Article |
| id | doaj-art-a9db792398f6483e8594e82496caa0e0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a9db792398f6483e8594e82496caa0e02025-02-03T01:21:40ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/20958052095805Periodicities of a System of Difference EquationsWeizhen Quan0Miaoqiao Pan1Xiaopei Li2Basic Education School, Lingnan Normal University, Zhanjiang, Guangdong 524037, ChinaBasic Education School, Lingnan Normal University, Zhanjiang, Guangdong 524037, ChinaBasic Education School, Lingnan Normal University, Zhanjiang, Guangdong 524037, ChinaWe study the periodicities of a system of difference equations xn+1=max1/xn,An/yn-k,yn+1=max1/yn,Bn/xn-k, where initial values (x-k,y-k),…,(x0,y0)∈(0,+∞)×(0,+∞). We show that if An,Bn∈(0,1) are two periodic sequences, then every solution of the above system is eventually periodic with period 2. If k is even, there must be one in xn and yn converges to period two solution.http://dx.doi.org/10.1155/2017/2095805 |
| spellingShingle | Weizhen Quan Miaoqiao Pan Xiaopei Li Periodicities of a System of Difference Equations Journal of Function Spaces |
| title | Periodicities of a System of Difference Equations |
| title_full | Periodicities of a System of Difference Equations |
| title_fullStr | Periodicities of a System of Difference Equations |
| title_full_unstemmed | Periodicities of a System of Difference Equations |
| title_short | Periodicities of a System of Difference Equations |
| title_sort | periodicities of a system of difference equations |
| url | http://dx.doi.org/10.1155/2017/2095805 |
| work_keys_str_mv | AT weizhenquan periodicitiesofasystemofdifferenceequations AT miaoqiaopan periodicitiesofasystemofdifferenceequations AT xiaopeili periodicitiesofasystemofdifferenceequations |