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.