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2013 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, E. S. Ismail
Abstr. Appl. Anal. 2013: 1-10 (2013). DOI: 10.1155/2013/179423

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.

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S. Atawna. R. Abu-Saris. I. Hashim. E. S. Ismail. "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 ) ." Abstr. Appl. Anal. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/179423

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1275.39004
MathSciNet: MR3055932
Digital Object Identifier: 10.1155/2013/179423

Rights: Copyright © 2013 Hindawi

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