Abstract
In this paper, we discuss some qualitative properties of the positive solutions to the following rational nonlinear difference equation x(n+1) = alpha-x(n-m)+delta x(u)/beta+gamma x(n-k)x(n-l)(x(n-k)+x(n-l)), n = 0, 1, 2, ...where the parameters alpha, beta, gamma, delta is an element of (0, infinity), while m, k, l are positive integers, such that m < k < l. The initial conditions x-(m), ..., x(-k), ..., x(-l), ..., x(-1), ..., x(0) are arbitrary positive real numbers. We will give some numerical examples to illustrate our results.