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AbstractIn this paper, we study the following max-type system of difference equations: {xn=max{An,yn−1xn−2},yn=max{Bn,xn−1yn−2},n∈{0,1,2,…},$$\textstyle\begin{cases}x_{n} = \max \{A_{n},\frac{y_{n-1}}{x_{n-2}} \},\\ y_{n} = \max \{B_{n} ,\frac{x_{n-1}}{y_{n-2}} \}, \end{cases}\displaystyle n\in \{0,1,2,\ldots\}, $$ where An,Bn∈(0,+∞)$A_{n},B_{n}\in(0, +\infty)$… Click to show full abstract
AbstractIn this paper, we study the following max-type system of difference equations: {xn=max{An,yn−1xn−2},yn=max{Bn,xn−1yn−2},n∈{0,1,2,…},$$\textstyle\begin{cases}x_{n} = \max \{A_{n},\frac{y_{n-1}}{x_{n-2}} \},\\ y_{n} = \max \{B_{n} ,\frac{x_{n-1}}{y_{n-2}} \}, \end{cases}\displaystyle n\in \{0,1,2,\ldots\}, $$ where An,Bn∈(0,+∞)$A_{n},B_{n}\in(0, +\infty)$ are periodic sequences with period 2 and the initial values x−1,y−1,x−2,y−2∈(0,+∞)$x_{-1},y_{-1},x_{-2},y_{-2}\in (0,+\infty)$. We show that every solution of the above system is eventually periodic.
Journal Title: Advances in Difference Equations
Year Published: 2018
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