On a solvable system of non-linear difference equations with variable coefficients

WOS:000637970300013In this paper, we show that the system of difference equations x(n) = x(n-2)z(n-3)/z(n-1)(a(n) + b(n)x(n-2)z(n-3)), y(n) = y(n-2)x(n-3)/x(n-1)(alpha(n) + beta(n)y(n-2)x(n-3)), z(n) = z(n-2)y(n-3)/y(n-1)(A(n) + B(n)z(n-2)y(n-3)), n is an element of N-0, where the sequences (a(n))(n is an element of N0), (b(n))(n is an element of N0), (alpha(n))(n is an element of N0), (beta(n))(n is an element of N0), (A(n))(n is an element of N0), (B-n)(n is an element of N0), and the initial values x(-j),y(-j),z(-j),j is an element of {1,2,3} are non-zero real numbers, can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system