On the Period‐Two Cycles of xn+1 = (α + βxn + γxn−k)/(A + Bxn + Cxn−k)

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

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We consider the higher order nonlinear rational difference equation xn+1 = (α + βxn + γxn−k)/(A + Bxn + Cxn−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, x0 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.

Date: 2013
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https://doi.org/10.1155/2013/179423

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:179423

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