Dynamics and Expression of Solution of a Sixth Order Difference Equation

Abstract

This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers and $\alpha ,\ \beta ,\ \gamma ,\ \delta \ $are positive constants. Also we obtain the closed form of the solutions of some special cases of this equation.