Dynamics of a second-order nonlinear difference system with exponents

Abstract In this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of positive solutions second-order difference system $$\begin{aligned} x_{n+1}&= \alpha _1 + a e ^{-x_{n-1}} b y_{n} ^{-y_{n-1}},\\ y_{n+1}&= _2 +c ^{-y_{n-1}}+ d x_{n} \quad n=0,1,2,\ldots \end{aligned}$$ x n + 1 = α a e - b y , 2 c d 0 … where $$\alpha _1, _2, a, , c,d$$ are real numbers initial conditions $$x_{-1},x_0, y_{-1}, y_0$$ arbitrary nonnegative numbers.