Abstract
We investigate the expressions of solutions and the periodicity nature of the following system of rational difference equations of order four
x(n+1) = z(n-3)/a(1)+b(1)z(n)y(n-1)x(n-2)z(n-3) , y(n+1) = x(n-3)/a(2)+b(2)x(n)z(n-1)y(n-2)x(n-3)
z(n+1) = y(n-3)/a(3)+b(3)y(n)x(n-1)z(n-2)y(n-3),
where the initial conditions x_3, x_2, x_1, x(0), y-3, Y-2, Y-1, y(0), z_3, z_2, z_1 and zo are arbitrary real numbers and a1, b1, a2, b2, a3, b3 are integers. (C) 2016 All rights reserved.