On a solvable system of difference equations of higher-order with period two coefficients

Abstract

We show that the next difference equations system

x_{n+1}=((a_{n}x_{n-k+1}y_{n-k})/(y_{n}-α_{n}))+β_{n+1}, y_{n+1}=((b_{n}y_{n-k+1}x_{n-k})/(x_{n}-β_{n}))+α_{n+1}, n∈N₀,

where N₀=N∪{0}, the sequences (a_{n})_{n∈N₀}, (b_{n})_{n∈N₀}, (α_{n})_{n∈N₀}, (β_{n})_{n∈N₀} are two periodic and the initial conditions x_{-i}, y_{-i}  i∈{0,1,…,k}, are non-zero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a₀=b₁ and a₁=b₀.

Keywords

• Periodic solution,solution in closed form system of difference equations

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