Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order
We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/8467682 |
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| author | Guangwang Su Taixiang Sun Bin Qin |
| author_facet | Guangwang Su Taixiang Sun Bin Qin |
| author_sort | Guangwang Su |
| collection | DOAJ |
| description | We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually. |
| format | Article |
| id | doaj-art-715772ea7a0048c59a7d81308e806fe7 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-715772ea7a0048c59a7d81308e806fe72025-02-03T06:12:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/84676828467682Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher OrderGuangwang Su0Taixiang Sun1Bin Qin2College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, ChinaWe study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.http://dx.doi.org/10.1155/2018/8467682 |
| spellingShingle | Guangwang Su Taixiang Sun Bin Qin Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order Discrete Dynamics in Nature and Society |
| title | Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order |
| title_full | Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order |
| title_fullStr | Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order |
| title_full_unstemmed | Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order |
| title_short | Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order |
| title_sort | eventually periodic solutions of a max type system of difference equations of higher order |
| url | http://dx.doi.org/10.1155/2018/8467682 |
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