Global dynamics of some system of second-order difference equations

In this paper, we study the boundedness and persistence of positive solution, existence of invariant rectangle, local and global behavior, and rate of convergence of positive solutions of the following systems of exponential difference equations {document}$ {align*} xₙ₊₁ = {α_1+β_1e^{-xₙ₋₁}}{γ_1+y_n},\ yₙ₊₁ = {α_2+β_2e^{-yₙ₋₁}}{γ_2+x_n},\\ xₙ₊₁ = {α_1+β_1e^{-yₙ₋₁}}{γ_1+x_n},\ yₙ₊₁ = {α_2+β_2e^{-xₙ₋₁}}{γ_2+y_n}, {align*} document where the parameters document α_i,\ β_i,\ γ_i document for document i ∈ \{1,2\} document and the initial conditions document x₋₁, x_0, y₋₁, y_0 ${document} are positive real numbers. Some numerical example are given to illustrate our theoretical results.