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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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2022-12-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2682359 |
| _version_ | 1797294120372273152 |
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| author | Mohamed Abd El-moneam |
| author_facet | Mohamed Abd El-moneam |
| author_sort | Mohamed Abd El-moneam |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-03-07T21:25:37Z |
| format | Article |
| id | doaj.art-2a634ac378e04e55a42a292c826f4e18 |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:25:37Z |
| publishDate | 2022-12-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-2a634ac378e04e55a42a292c826f4e182024-02-27T04:38:36ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012022-12-015418919810.33434/cams.11828611225On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$Mohamed Abd El-moneam0Mathematics Department, Faculty of Science, Jazan University, Kingdom of Saudi Arabia.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 $mhttps://dergipark.org.tr/tr/download/article-file/2682359difference equationsqualitative properties of solutions of difference equationsrational difference equationsglobally asymptotically stable\ prime period two solution.equilibrium |
| spellingShingle | Mohamed Abd El-moneam On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ Communications in Advanced Mathematical Sciences difference equations qualitative properties of solutions of difference equations rational difference equations globally asymptotically stable \ prime period two solution. equilibrium |
| title | On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ |
| title_full | On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ |
| title_fullStr | On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ |
| title_full_unstemmed | On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ |
| title_short | On the Global of the Difference Equation ${x_{n+1}}=\frac{{\alpha {x_{n-m}+\eta {x_{n-k}}+}}\delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$ |
| title_sort | 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 |
| topic | difference equations qualitative properties of solutions of difference equations rational difference equations globally asymptotically stable \ prime period two solution. equilibrium |
| url | https://dergipark.org.tr/tr/download/article-file/2682359 |
| work_keys_str_mv | AT mohamedabdelmoneam ontheglobalofthedifferenceequationxn1fracalphaxnmetaxnkdeltaxnbetagammaxnkxnlleftxnkxnlright |