Qualitative Behavior of an Exponential Symmetric Difference Equation System

We examine the unboundedness, persistence, boundedness, uniqueness, and existence of non-negative equilibrium of an exponential symmetric difference equations system: Ωn+1=α1+β1Ωn+γ1Ωn−1e−(Ωn+ϖn), ϖn+1=α2+β2ϖn+γ2ϖn−1e−(Ωn+ϖn),n=0,1,⋯, whereby initial values Ω−1,ϖ−1,Ω0,ϖ0 and parameters α1,α2 are non-negative real numbers and β1,β2∈(0,1) and γ1,γ2≤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.