Dynamics of a second-order nonlinear difference system with exponents. (English) Zbl 1479.39011
Summary: In this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of the positive solutions of the second-order difference system
\[
\begin{aligned}
x_{n+1} &= \alpha_1 + a e^{-x_{n-1}} + b y_n e^{-y_{n-1}}, \\
y_{n+1} &= \alpha_2 +c e^{-y_{n-1}}+ d x_n e^{-x_{n-1}}, \quad n=0,1,2,\ldots
\end{aligned}
\]
where \(\alpha_1, \alpha_2, a, b, c,d\) are positive real numbers and the initial conditions \(x_{-1},x_0, y_{-1}, y_0\) are arbitrary nonnegative numbers.
MSC:
| 39A22 | Growth, boundedness, comparison of solutions to difference equations |
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