Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$
The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of all admissible solutions of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$, n=0,1,2,... where A, B, C are positive real numbers.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2013-11-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/14432 |
| _version_ | 1818132946149703680 |
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| author | R. Abo-Zeid Cengiz Cinar |
| author_facet | R. Abo-Zeid Cengiz Cinar |
| author_sort | R. Abo-Zeid |
| collection | DOAJ |
| description | The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of all admissible solutions of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$, n=0,1,2,... where A, B, C are positive real numbers. |
| first_indexed | 2024-12-11T08:44:54Z |
| format | Article |
| id | doaj.art-0052140f12164638873532355da09b4f |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-11T08:44:54Z |
| publishDate | 2013-11-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-0052140f12164638873532355da09b4f2022-12-22T01:14:10ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882013-11-01311434910.5269/bspm.v31i1.144327484Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$R. Abo-Zeid0Cengiz Cinar1October 6 university Faculty of Engineering Department of Basic ScienceSelcuk University Faculty of Education Mathematics DepartmentThe aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of all admissible solutions of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$, n=0,1,2,... where A, B, C are positive real numbers.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/14432difference equationperiodic solutionglobally asymptotically stable |
| spellingShingle | R. Abo-Zeid Cengiz Cinar Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ Boletim da Sociedade Paranaense de Matemática difference equation periodic solution globally asymptotically stable |
| title | Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ |
| title_full | Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ |
| title_fullStr | Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ |
| title_full_unstemmed | Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ |
| title_short | Global behavior of the difference equation $x_{n+1}=\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$ |
| title_sort | global behavior of the difference equation x n 1 frac ax n 1 b cx n x n 2 |
| topic | difference equation periodic solution globally asymptotically stable |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/14432 |
| work_keys_str_mv | AT rabozeid globalbehaviorofthedifferenceequationxn1fracaxn1bcxnxn2 AT cengizcinar globalbehaviorofthedifferenceequationxn1fracaxn1bcxnxn2 |