On solutions of the difference equation x n + 1 = x n - 3 / ( - 1 + x n x n - 1 x n - 2 x n - 3 )

Cengiz Cinar; Ramazan Karatas; Ibrahim Yalçınkaya

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 3, page 257-261
  • ISSN: 0862-7959

Abstract

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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 , ⋯ where x - 3 , x - 2 , x - 1 and x 0 are real numbers such that x 0 x - 1 x - 2 x - 3 ≠ 1 .

How to cite

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Cinar, Cengiz, Karatas, Ramazan, and Yalçınkaya, Ibrahim. "On solutions of the difference equation $x_{n+1}=x_{n-3}/(-1+x_{n}x_{n-1}x_{n-2}x_{n-3})$." Mathematica Bohemica 132.3 (2007): 257-261. <http://eudml.org/doc/250263>.

@article{Cinar2007,
abstract = {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 $x_\{0\}x_\{-1\}x_\{-2\}x_\{-3\}\ne 1.$},
author = {Cinar, Cengiz, Karatas, Ramazan, Yalçınkaya, Ibrahim},
journal = {Mathematica Bohemica},
keywords = {difference equation; recursive sequence; solutions; equilibrium point; recursive sequence; equilibrium point; rational difference equation},
language = {eng},
number = {3},
pages = {257-261},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On solutions of the difference equation $x_\{n+1\}=x_\{n-3\}/(-1+x_\{n\}x_\{n-1\}x_\{n-2\}x_\{n-3\})$},
url = {http://eudml.org/doc/250263},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Cinar, Cengiz
AU - Karatas, Ramazan
AU - Yalçınkaya, Ibrahim
TI - On solutions of the difference equation $x_{n+1}=x_{n-3}/(-1+x_{n}x_{n-1}x_{n-2}x_{n-3})$
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 3
SP - 257
EP - 261
AB - 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 $x_{0}x_{-1}x_{-2}x_{-3}\ne 1.$
LA - eng
KW - difference equation; recursive sequence; solutions; equilibrium point; recursive sequence; equilibrium point; rational difference equation
UR - http://eudml.org/doc/250263
ER -

References

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  1. Dynamics of a kth order rational difference equation, Appl. Math. Comput. (In press.). 
  2. The rational recursive sequence x n + 1 = b x n 2 / 1 + x n - 1 2 , Comput. Math. Appl. 28 (1994), 37–43. (1994) MR1284218
  3. On the positive solutions of the difference equation x n + 1 = x n - 1 / ( 1 + x n × x n - 1 ) , Appl. Math. Comput. 150 (2004), 21–24. (2004) MR2034364
  4. On the positive solutions of the difference equation x n + 1 = a x n - 1 / ( 1 + b x n × x n - 1 ) , Appl. Math. Comput. 156 (2004), 587–590. (2004) MR2087535
  5. On the difference equation x n + 1 = x n - 1 / ( - 1 + x n x n - 1 ) , Appl. Math. Comput. 158 (2004), 813–816. (2004) MR2095706
  6. 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. (2004) MR2077785
  7. 10.11650/twjm/1500558306, Taiwanese J. Math. 6 (2002), 405–414. (2002) Zbl1019.39010MR1921603DOI10.11650/twjm/1500558306
  8. 10.1007/BF02936567, J. Appl. Math. Comput. 18 (2005), 229–234. (2005) MR2137703DOI10.1007/BF02936567
  9. On the recursive sequences x n + 1 = a x n - 1 + b x n - 2 / ( c + d x n - 1 x n - 2 ) , Appl. Math. Comput. 162 (2005), 1485–1497. (2005) MR2113984

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