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

Authors : Yasin YAZLİK, Merve KARA

Pages : 1675-1693

Doi:10.31801/cfsuasmas.548262

View : 16 | Download : 9

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :We show that the next difference equations system x_{n+1}=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(a_{n}x_{n-k+1}y_{n-k});/insert ignore into journalissuearticles values(y_{n}-α_{n}););+β_{n+1}, y_{n+1}=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(b_{n}y_{n-k+1}x_{n-k});/insert ignore into journalissuearticles values(x_{n}-β_{n}););+α_{n+1}, n∈N₀, where N₀=N∪{0}, the sequences insert ignore into journalissuearticles values(a_{n});_{n∈N₀}, insert ignore into journalissuearticles values(b_{n});_{n∈N₀}, insert ignore into journalissuearticles values(α_{n});_{n∈N₀}, insert ignore into journalissuearticles values(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