Global dynamics of some system of second-order difference equations

<p style='text-indent:20px;'>In this paper, we study the boundedness and persistence of positive solution, existence invariant rectangle, local global behavior, rate convergence solutions following systems exponential difference equations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> $ \begin{align*} x_{n+1} = \dfrac{\alpha_1+\beta_1e^{-x_{n-1}}}{\gamma_1+y_n},\ y_{n+1} \dfrac{\alpha_2+\beta_2e^{-y_{n-1}}}{\gamma_2+x_n},\\ \dfrac{\alpha_1+\beta_1e^{-y_{n-1}}}{\gamma_1+x_n},\ \dfrac{\alpha_2+\beta_2e^{-x_{n-1}}}{\gamma_2+y_n}, \end{align*} </tex-math></disp-formula></p><p style='text-indent:20px;'>where parameters <inline-formula><tex-math id="M1">$ \alpha_i,\ \beta_i,\ \gamma_i $</tex-math></inline-formula> for id="M2">$ i \in \{1,2\} initial conditions id="M3">$ x_{-1}, x_0, y_{-1}, y_0 are real numbers. Some numerical example given to illustrate our theoretical results.</p>