On the global attractivity of two nonlinear difference equations |
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Authors: | E M E Zayed M A El-Moneam |
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Institution: | 1.Mathematics Department, Faculty of Science,Taif University,El-Taif,Kingdom of Saudi Arabia;2.Mathematics Department, Faculty of Science,Zagazig University,Zagazig,Egypt |
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Abstract: | The main objective of this paper is to study some qualitative behavior of the solutions of the two difference equations $ {x_{n + 1}} = {{{a{x_n} - b{x_{n - k}}}} \left/ {{\left( {c{x_n} - d{x_{n - k}}} \right)}} \right.}\quad n = 0,\,1,\,2, \ldots, $ and $ {x_{n + 1}} = {{{a{x_{n - k}} + b{x_n}}} \left/ {{\left( {c{x_n} - d{x_{n - k}}} \right)}} \right.}\quad n = 0,\,1,\,2, \ldots, $ where the initial conditions x???k, ? , x???1 , x0 are arbitrary positive real numbers and the coefficients a, b, c, and d are positive constants, while k is a positive integer number. |
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