$On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$$

On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$

In this article, we consider and discuss some properties of the positive solutions to the following rational nonlinear DE ${x_{n+1}}=\frac{{\alpha { x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}} \left( {{x_{n-k}}+{x_{n-l}}}\right) }}$, $n=0,1,...,$ where the parameters...

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Bibliographic Details
Main Author:	Mohamed Abd El-moneam
Format:	Article
Language:	English
Published:	Emrah Evren KARA 2022-12-01
Series:	Communications in Advanced Mathematical Sciences
Subjects:	difference equations qualitative properties of solutions of difference equations rational difference equations globally asymptotically stable \ prime period two solution. equilibrium
Online Access:	https://dergipark.org.tr/tr/download/article-file/2682359

Description
Summary:	In this article, we consider and discuss some properties of the positive solutions to the following rational nonlinear DE ${x_{n+1}}=\frac{{\alpha { x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}} \left( {{x_{n-k}}+{x_{n-l}}}\right) }}$, $n=0,1,...,$ where the parameters $ \alpha ,\beta ,\gamma ,\delta ,{\eta }\in (0,\infty )$, while $m,k,l$ are positive integers, such that $m
ISSN:	2651-4001

On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$

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