Global convergence properties of first-order homogeneous systems of rational difference equations

Abstract

We establish the global convergence properties of the homogeneous system for all non-negative coefficients and C 2, and for all positive initial conditions. In order to prove these results, we reduce the problem to the study of a first-order rational difference equation of one variable that is quadratic in the numerator and the denominator. We also prove the convergence properties for a more general class of first-order equations, which we apply to our rational difference equation.