On the recursive sequence 20 1 2 5 8 11 14 17

Abstract

The behaivour of the solutions of the following system of difference equations is examined, 20 1 2 5 8 11 14 17 1 n n nnnn n n x x xxxx x x ? + ???? ? ? = + , where the initial conditions are positive real numbers. The initial conditions of the equation are arbitrary positive real numbers. Also, we discuss and illustrate the stability of the solutions in the neighborhood of the critical points and the periodicity of the considered equations.