| 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 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
257-261 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.2007.134123 |
| . |
| Date available:
|
2009-09-24T22:31:38Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134123 |
| . |
| 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, 10.11650/twjm/1500558306 |
| 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, 10.1007/BF02936567 |
| 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 |
| . |
