Abstract and Applied Analysis

On the Period-Two Cycles of x n + 1 = ( α + β x n + γ x n - k ) / ( A + B x n + C x n - k )

S. Atawna, R. Abu-Saris, I. Hashim, and E. S. Ismail

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Abstract

We consider the higher order nonlinear rational difference equation x n + 1 = ( α + β x n + γ x n - k ) / ( A + B x n + C x n - k ) , n = 0,1 , 2 , , where the parameters α , β , γ , A , B , C are positive real numbers and the initial conditions x - k , , x - 1 , x 0 are nonnegative real numbers, k { 1,2 , } . We give a necessary and sufficient condition for the equation to have a prime period-two solution. We show that the period-two solution of the equation is locally asymptotically stable.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 179423, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511884

Digital Object Identifier
doi:10.1155/2013/179423

Mathematical Reviews number (MathSciNet)
MR3055932

Zentralblatt MATH identifier
1275.39004

Citation

Atawna, S.; Abu-Saris, R.; Hashim, I.; Ismail, E. S. On the Period-Two Cycles of ${x}_{n+1}=\left(\alpha +\beta {x}_{n}+\gamma {x}_{n-k}\right)/\left(A+B{x}_{n}+C{x}_{n-k}\right)$. Abstr. Appl. Anal. 2013 (2013), Article ID 179423, 10 pages. doi:10.1155/2013/179423. https://projecteuclid.org/euclid.aaa/1393511884


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