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

Year 2022, Volume: 5 Issue: 4, 189 - 198, 30.12.2022

Mohamed Abd El-moneam

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

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

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