Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients

This paper is dealt with the following system of difference equations x(n+1) = (a(n)/x(n)) + (b(n)/y(n)), y(n+1) = (c(n)/x(n)) + (d(n)/y(n)), where n is an element of N-0 = N boolean OR {0}, the initial values x(0) and y(0) are the positive real numbers, and the sequences (a(n))(n >= 0), (b(n))(n >= 0), (c(n))(n >= 0), and (d(n))(n >= 0) are two-periodic and positive. The system is an extension of a system where every positive solution is two-periodic or converges to a two-periodic solution. Here, the long-term behavior of positive solutions of the system is examined by using a new method to solve the system.