Journal of innovative applied mathematics and computational sciences
Volume 2, Numéro 1, Pages 78-91
2022-06-30
The Expressions And Behavior Of Solutions For Nonlinear Systems Of Rational Difference Equations
Authors : Elsayed Elsayed Mohamed . Alharbi Kholoud N. .
Abstract
In this paper, we investigate the form of the solutions of the following systems of difference equations of second order \begin{eqnarray*} x_{n+1} &=&\frac{x_{n}y_{n-1}}{x_{n}+y_{n}},\quad y_{n+1}=\frac{x_{n-1}y_{n}}{% x_{n}+y_{n}}, \\ x_{n+1} &=&\frac{x_{n}y_{n-1}}{x_{n}-y_{n}},\quad y_{n+1}=\frac{x_{n-1}y_{n}}{% x_{n}-y_{n}},\ \ \ n=0,1,..., \end{eqnarray*}% {\Large \noindent} where the initial conditions $x_{-1},\ x_{0},\ y_{-1}\ $% and\ $\ y_{0}$ are arbitrary nonzero real numbers.
Keywords
Periodic solution, boundedness, systems of difference equations.
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