Abstract In this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of positive solutions second-order difference system $$\begin{aligned} x_{n+1}&amp;= \alpha _1 + a e ^{-x_{n-1}} b y_{n} ^{-y_{n-1}},\\ y_{n+1}&amp;= _2 +c ^{-y_{n-1}}+ d x_{n} \quad n=0,1,2,\ldots \end{aligned}$$ <mml:mr...

&lt;p style='text-indent:20px;'&gt;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&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; $ \begin{align*} x_{n+1} = \dfrac{\alpha_1+\be...