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Title: On solutions of the difference equation $x_{n+1}=x_{n-3}/(-1+x_{n}x_{n-1}x_{n-2}x_{n-3})$ (English)
Author: Cinar, Cengiz
Author: Karatas, Ramazan
Author: Yalçınkaya, Ibrahim
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 132
Issue: 3
Year: 2007
Pages: 257-261
Summary lang: English
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Category: math
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Summary: We study the solutions and attractivity of the difference equation $x_{n+1}={x_{n-3}}/{(-1+x_{n}x_{n-1}x_{n-2}x_{n-3})}$ for $n=0,1,2,\dots $ where $x_{-3},x_{-2},x_{-1}$ and $x_{0}$ are real numbers such that $x_{0}x_{-1}x_{-2}x_{-3}\ne 1.$ (English)
Keyword: difference equation
Keyword: recursive sequence
Keyword: solutions
Keyword: equilibrium point
MSC: 39A11
MSC: 39A20
idZBL: Zbl 1174.39303
idMR: MR2355658
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Date available: 2009-09-24T22:31:38Z
Last updated: 2012-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/134123
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Reference: [1] Aloqeili M.: Dynamics of a kth order rational difference equation.Appl. Math. Comput. (In press.).
Reference: [2] Camouzis E., Ladas G., Rodrigues I. W., Northshield S.: The rational recursive sequence $x_{n+1}={bx_{n}^{2}}/{1+x_{n-1}^{2}}$.Comput. Math. Appl. 28 (1994), 37–43. MR 1284218
Reference: [3] Cinar C.: On the positive solutions of the difference equation $ x_{n+1}={x_{n-1}}/(1+x_{n}\times x_{n-1})$.Appl. Math. Comput. 150 (2004), 21–24. MR 2034364
Reference: [4] Cinar C.: On the positive solutions of the difference equation $ x_{n+1}=ax_{n-1}/(1+bx_{n}\times x_{n-1})$.Appl. Math. Comput. 156 (2004), 587–590. MR 2087535
Reference: [5] Cinar C.: On the difference equation $ x_{n+1}=x_{n-1}/(-1+x_{n}x_{n-1})$.Appl. Math. Comput. 158 (2004), 813–816. MR 2095706
Reference: [6] Stevic S.: More on a rational recurence relation $ x_{n+1}={x_{n-1}}/(1+x_{n-1}x_{n})$.Appl. Math. E-Notes 4 (2004), 80–84. MR 2077785
Reference: [7] Stevic S.: On the recursive sequence $x_{n+1}={x_{n-1}}/{ g(x_{n})}$.Taiwanese J. Math. 6 (2002), 405–414. Zbl 1019.39010, MR 1921603
Reference: [8] Stevic S.: On the recursive sequence $x_{n+1}=\alpha +{x_{n-1}^{p}}/{x_{n}^{p}}$.J. Appl. Math. Comput. 18 (2005), 229–234. MR 2137703
Reference: [9] Yang X., Su W., Chen B., Megson G., Evans D.: On the recursive sequences $x_{n+1}={ax_{n-1}+bx_{n-2}}/({c+dx_{n-1}x_{n-2}})$.Appl. Math. Comput. 162 (2005), 1485–1497. MR 2113984
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