Dynamics of a third-order rational difference equation

In this paper, we study the global behavior of positive solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-1}}{C+Dx^p_nx^q_{n-2}}, n=0, 1, ...,$ where the initial conditions x0, x–1, x–2, and the parameter B are nonnegative real numbers, the parameters A, C, D are positive real numbers and...

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Bibliographic Details
Published in:Bulletin mathématiques de la Société des sciences mathématiques de Roumanie 2016-01, Vol.59(107) (1), p.13-22
Main Authors: Belhannache, Farida, Touafek, Nouressadat, Abo-Zeid, Raafat
Format: Article
Language:English
Subjects:
Difference equations
Global behavior
Real numbers
Online Access:Get full text
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Summary:In this paper, we study the global behavior of positive solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-1}}{C+Dx^p_nx^q_{n-2}}, n=0, 1, ...,$ where the initial conditions x0, x–1, x–2, and the parameter B are nonnegative real numbers, the parameters A, C, D are positive real numbers and p, q are fixed positive integers.
ISSN:1220-3874
2065-0264