On the solutions of a max-type system of difference equations of higher order

[摘要] In this paper, we study the following max-type system of difference equations of higher order: $$ \textstyle\begin{cases} x_{n} = \max \{A ,\frac{y_{n-t}}{x_{n-s}} \}, \\ y_{n} = \max \{B ,\frac{x_{n-t}}{y_{n-s}} \},\end{cases}\displaystyle \quad n\in \{0,1,2,\ldots \}, $$ where $A,B\in (0, +\infty )$, $t,s\in \{1,2,\ldots \}$ with $\gcd (s,t)=1$, the initial values $x_{-d},y_{-d},x_{-d+1},y_{-d+1}, \ldots , x_{-1}, y_{-1}\in (0,+ \infty )$ and $d=\max \{t,s\}$.

[学科分类] 航空航天科学

[关键词] Max-type system of difference equations;Solution;Eventual periodicity