Stability and Periodic Nature of a System of Difference Equations

In this paper, we investigate the equilibrium points of following a system of difference equations x_{n+۱}=x_{n-۲}y_{n}-۱,y_{n+۱}=y_{n-۲}x_{n}-۱. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

Keywords:

Difference equations , discrete dynamical systems , equilibrium points , stability , periodicity , invariant