Original Article
Kyungpook Mathematical Journal 2010; 50(4): 483-497
Published online December 23, 2010
Copyright © Kyungpook Mathematical Journal.
Dynamics of Recursive Sequence of Order Two
Elsayed Mohammed Elsayed
King AbdulAziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Received: December 23, 2010; Revised: December 23, 2010; Accepted: December 23, 2010
In this paper we study some qualitative behavior of the solutions of the
difference equation
egin{equation*}
x_{n+1}=ax_{n}+dfrac{bx_{n}}{cx_{n}-dx_{n-1}},;;;n=0,1,...,
end{equation*}%
where the initial conditions $x_{-1},;x_{0};$are arbitrary real numbers and%
$;a,b,c,d;$are positive constants with $cx_{0}-dx_{-1}
eq 0$.
Keywords: difference equations, stability, periodicity, solution of the difference
equation