Qualitative Behavior of the difference equation ${x_{n+1}}=\\frac{{ \\alpha {x_{n-m}+\\eta {x_{n-k}{+\\sigma {x_{n-l}}}}+}}\\delta {{x_{n}}}}{{\\beta +\\gamma {x_{n-k}}{x_{n-l}}\\left( {{x_{n-k}}+{x_{n-l}}}\\right) }}$

Authors : Mohamed ABD ELMONEAM

Pages : 128-136

Doi:10.33401/fujma.1239100

View : 51 | Download : 56

Publication Date : 2023-06-30

Article Type : Research Paper

Abstract :In this paper, we discuss some qualitative properties of the positive solutions to the following rational nonlinear difference equation ${x_{n+1}}=% \\frac{{\\alpha {x_{n-m}+\\eta {x_{n-k}{+\\sigma {x_{n-l}}}}+}}\\delta {{x_{n}}}}{% {\\beta +\\gamma {x_{n-k}}{x_{n-l}}\\leftinsert ignore into journalissuearticles values( {{x_{n-k}}+{x_{n-l}}}\\right); }}$, $% n=0,1,2,...$ where the parameters $\\alpha ,\\beta ,\\gamma ,\\delta ,{\\eta },{% \\sigma }\\in insert ignore into journalissuearticles values(0,\\infty );$, while $m,k,l$ are positive integers, such that $% m
Keywords : Difference equations, Rational difference equations, qualitative properties of solutions of difference equations, Equilibrium, Globally asymptotically stable, Oscillates, Prime period two solution