On the system of difference equations

Abstract

In this paper, we show that the system of difference equations

x(n) = x(n-2)y(n-3)/y(n-1)(a(n)+b(n)x(n-2)y(n-3)), y(n) = y(n-2)x(n-3)/x(n-1)(alpha(n)+beta(n)y(n-2)x(n-3)), n is an element of N-0,

where the sequences for all n is an element of N-0, (a(n)), (b(n)), (alpha(n)), (beta(n)) and the initial values x(-j), y(-j), j is an element of {1, 2, 3} are non-zero real numbers, can be solved in the closed form. For the case when all the sequences (a(n)), (b(n)), (alpha(n)), (beta(n)) are constant we describe the asymptotic behavior and periodicity of solutions of above system is also investigated.