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Keywords:
difference equation; recursive sequence; solutions; equilibrium point
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 $x_{0}x_{-1}x_{-2}x_{-3}\ne 1.$
References:
[1] Aloqeili M.: Dynamics of a kth order rational difference equation. Appl. Math. Comput. (In press.).
[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
[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
[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
[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
[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
[7] Stevic S.: On the recursive sequence $x_{n+1}={x_{n-1}}/{ g(x_{n})}$. Taiwanese J. Math. 6 (2002), 405–414. MR 1921603 | Zbl 1019.39010
[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
[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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