On a System of k-Difference Equations of Order Three

In this paper, we deal with the global behavior of the positive solutions of the system of k-difference equations u(n+1)((1)) = (alpha(1)u(n-1)((1))/beta(1) + alpha(1)(u(n-2)((2)))(r1)), u(n+1)((2)) = alpha(2)u(n-1)((2))/beta(2) + alpha(2)(u(n-2)((3)))(r2), ... , u(n+1)((k)) = alpha(k)u(n-1)((k))/beta(k) + alpha(k)(u(n-2)((1)))(rk), n is an element of N-0, where the initial conditions u(-l)((i)) (l = 0, 1, 2) are nonnegative real numbers and the parameters alpha(i), beta(i), gamma(i), and r(i) are positive real numbers for i = 1, 2, ... , k, by extending some results in the literature. By the end of the paper, we give three numerical examples to support our theoretical results related to the system with some restrictions on the parameters.