Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}
In this paper we consider the difference equation \[x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...\tag{E}\] with positive parameters \(a\) and \(c\), negative parameter \(b\) and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation \(\text{(E)}\)...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2006-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol26/3/art/opuscula_math_2628.pdf |
| _version_ | 1811327206582910976 |
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| author | Anna Andruch-Sobiło Małgorzata Migda |
| author_facet | Anna Andruch-Sobiło Małgorzata Migda |
| author_sort | Anna Andruch-Sobiło |
| collection | DOAJ |
| description | In this paper we consider the difference equation \[x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...\tag{E}\] with positive parameters \(a\) and \(c\), negative parameter \(b\) and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation \(\text{(E)}\). |
| first_indexed | 2024-04-13T15:03:42Z |
| format | Article |
| id | doaj.art-cc6fa756722c41bbbe03df089b8f0ebf |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-04-13T15:03:42Z |
| publishDate | 2006-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-cc6fa756722c41bbbe03df089b8f0ebf2022-12-22T02:42:14ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742006-01-012633873942628Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}Anna Andruch-Sobiło0Małgorzata Migda1Poznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, PolandPoznań University of Technology, Institute of Mathematics, Piotrowo 3A, 60-965 Poznań, PolandIn this paper we consider the difference equation \[x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...\tag{E}\] with positive parameters \(a\) and \(c\), negative parameter \(b\) and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation \(\text{(E)}\).http://www.opuscula.agh.edu.pl/vol26/3/art/opuscula_math_2628.pdfdifference equationexplicit formulapositive solutionsasymptotic stability |
| spellingShingle | Anna Andruch-Sobiło Małgorzata Migda Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} Opuscula Mathematica difference equation explicit formula positive solutions asymptotic stability |
| title | Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} |
| title_full | Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} |
| title_fullStr | Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} |
| title_full_unstemmed | Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} |
| title_short | Further properties of the rational recursive sequence x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}} |
| title_sort | further properties of the rational recursive sequence x n 1 frac ax n 1 b cx n x n 1 |
| topic | difference equation explicit formula positive solutions asymptotic stability |
| url | http://www.opuscula.agh.edu.pl/vol26/3/art/opuscula_math_2628.pdf |
| work_keys_str_mv | AT annaandruchsobiło furtherpropertiesoftherationalrecursivesequencexn1fracaxn1bcxnxn1 AT małgorzatamigda furtherpropertiesoftherationalrecursivesequencexn1fracaxn1bcxnxn1 |