Dynamics of a second-order system of nonlinear difference equations

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equationsx_{n+۱}=x_{n-۱}y_{n}-۱,y_{n+۱}=y_{n-۱}x_{n}-۱n=۰,۱,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

Keywords:

difference equation , stability , Global Stability , periodicity , eventually periodicity