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 ELMONEAM

Pages : 189-198

Doi:10.33434/cams.1182861

View : 12 | Download : 10

Publication Date : 2022-12-30

Article Type : Research Paper

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