On the period-two cycles of xn+1 = (α + βx n + γxn-k)/(A + Bxn + Cxn-k)

S. Atawna; R. Abu-Saris; I. Hashim; E. S. Ismail

doi:10.1155/2013/179423

On the period-two cycles of x_n+1 = (α + βx _n + γx_n-k)/(A + Bx_n + Cx_n-k)

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

Universiti Kebangsaan Malaysia
King Saud bin Abdulaziz University for Health Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the higher order nonlinear rational difference equation x n + 1 = (α + βx_n + γx_n-k)/(A + Bx_n + Cx_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, x₀ are nonnegative real numbers, k ε {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.

Original language	English
Article number	179423
Journal	Abstract and Applied Analysis
Volume	2013
DOIs	https://doi.org/10.1155/2013/179423
State	Published - 2013
Externally published	Yes

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title = "On the period-two cycles of xn+1 = (α + βx n + γxn-k)/(A + Bxn + Cxn-k)",

abstract = "We consider the higher order nonlinear rational difference equation x n + 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 ε \{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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year = "2013",

doi = "10.1155/2013/179423",

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AU - Atawna, S.

AU - Abu-Saris, R.

AU - Hashim, I.

AU - Ismail, E. S.

PY - 2013

Y1 - 2013

N2 - We consider the higher order nonlinear rational difference equation x n + 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 ε {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.

AB - We consider the higher order nonlinear rational difference equation x n + 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 ε {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.

UR - https://www.scopus.com/pages/publications/84878683217

U2 - 10.1155/2013/179423

DO - 10.1155/2013/179423

M3 - Article

AN - SCOPUS:84878683217

SN - 1085-3375

VL - 2013

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 179423

ER -

On the period-two cycles of x_n+1 = (α + βx _n + γx_n-k)/(A + Bx_n + Cx_n-k)

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