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ON THE QUALITATIVE BEHAVIOURS OF A SECOND ORDER QUADRATIC RATIONAL DIFFERENCE EQUATION
Author(s) : I. M. Alsulami and E. M. Elsayed
Pages : [153] - [172]
Received : December 7, 2021; Revised April 9, 2022
Communicated by : Professor Emrullah Yasar
Pages : [153] - [172]
Received : December 7, 2021; Revised April 9, 2022
Communicated by : Professor Emrullah Yasar
Abstract
The aim of this article is to give a clear analyze of local and global stability and periodicity of the solutions of the following quadratic rational difference equation:
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where the initial conditions .gif){kind=small}
and .gif){kind=small}
are nonzero real numbers and the coefficients .gif){kind=small}
and ß.gif){kind=small}
are positive. Also, we confirm our theoretical results numerically by using MATLAB software.
Keywords
periodicity, stability, equilibrium point, global asymptotic, difference equations.