# Dynamics of Recursive Sequence of Order Two

Elsayed, Elsayed Mohammed

• Received : 2010.04.04
• Accepted : 2010.12.08
• Published : 2010.12.31
• 18 9

#### Abstract

In this paper we study some qualitative behavior of the solutions of the difference equation $x_{n+1}=ax_n=\frac{bx_n}{cx_n-dx_{n-1}}$, n=0,1,$\ldots$, where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants with $cx_0-dx_{-1}\neq0$.

#### Keywords

difference equations;stability;periodicity;solution of the difference equation

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