Abstract
We examine the unboundedness, persistence, boundedness, uniqueness, and existence of non-negative equilibrium of an exponential symmetric difference equations system: omega n+1=alpha 1+beta 1 omega n+gamma 1 omega n-1e-(omega n+pi n), pi n+1=alpha 2+beta 2 pi n+gamma 2 pi n-1e-(omega n+pi n), n=0,1,MIDLINE HORIZONTAL ELLIPSIS, whereby initial values omega-1,pi-1,omega 0,pi 0 and parameters alpha 1,alpha 2 are non-negative real numbers and beta 1,beta 2 & ISIN;(0,1) and gamma 1,gamma 2 & LE;0. We will discuss asymptotic global and local stability and the convergence rate of this system. Ultimately, to check our results, we set out some numerical explanations.