- Communications in Advanced Mathematical Sciences
- Vol: 5 Issue: 4
- On the Global of the Difference Equation ${x_{n+1}}=\\frac{{\\alpha {x_{n-m}+\\eta {x_{n-k}}+}}\\del...
On the Global of the Difference Equation ${x_{n+1}}=\\frac{{\\alpha {x_{n-m}+\\eta {x_{n-k}}+}}\\delta {{x_{n}}}}{{\\beta +\\gamma {x_{n-k}}{x_{n-l}}\\left( {{x_{n-k}}+{x_{n-l}}}\\right) }}$
Authors : Mohamed Abd El-moneam
Pages : 189-198
Doi:10.33434/cams.1182861
View : 11 | Download : 6
Publication Date : 2022-12-30
Article Type : Research
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 $mKeywords : Difference equations, Qualitative properties of solutions of difference equations, Rational difference equations, Globally asymptotically stable, \\ Prime period two solution., Equilibrium