Farida Belhannache, Nouressadat Touafek and Raafat Abo-Zeid: Dynamics of a third-order rational difference equation, p.13-22

Abstract:

In this paper, we study the global behavior of positive solutions of the difference equation $$x_{n+1}=\frac{A+B x_{n-1}}{C+D x_{n}^{p}x_{n-2}^{q}},\text{ }n=0,1,...,$$ 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.

Key Words: Difference equation, stability, global behavior, oscillatory.

2000 Mathematics Subject Classification: Primary: 39A10,
Secondary: 40A05.