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

Mohamed Abd El-moneam

doi:10.33434/cams.1182861

EN

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

Abstract

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

Keywords

Difference equations, Qualitative properties of solutions of difference equations, Rational difference equations, Globally asymptotically stable, \ Prime period two solution., Equilibrium

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mohamed Abd El-moneam ^*
Egypt

Publication Date

December 30, 2022

Submission Date

October 1, 2022

Acceptance Date

November 21, 2022

Published in Issue

Year 2022 Volume: 5 Number: 4

DOI

https://doi.org/10.33434/cams.1182861

IZ

https://izlik.org/JA63WA67DB

APA

Abd El-moneam, M. (2022). 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, 5(4), 189-198. https://doi.org/10.33434/cams.1182861

AMA

1.Abd El-moneam M. 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. 2022;5(4):189-198. doi:10.33434/cams.1182861

Chicago

Abd El-moneam, Mohamed. 2022. “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 5 (4): 189-98. https://doi.org/10.33434/cams.1182861.

EndNote

Abd El-moneam M (December 1, 2022) 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 5 4 189–198.

IEEE

[1]M. 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, vol. 5, no. 4, pp. 189–198, Dec. 2022, doi: 10.33434/cams.1182861.

ISNAD

Abd El-moneam, Mohamed. “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 5/4 (December 1, 2022): 189-198. https://doi.org/10.33434/cams.1182861.

JAMA

1.Abd El-moneam M. 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. 2022;5:189–198.

MLA

Abd El-moneam, Mohamed. “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, vol. 5, no. 4, Dec. 2022, pp. 189-98, doi:10.33434/cams.1182861.

Vancouver

1.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. 2022 Dec. 1;5(4):189-98. doi:10.33434/cams.1182861

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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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