Advances in Difference Equations
Volume 2004 (2004), Issue 2, Pages 121-139

Rate of convergence of solutions of rational difference equation of second order

S. Kalabušić and M. R. S. Kulenović

Department of Mathematics, University of Rhode Island, Kingston 02881-0816, RI, USA

Received 13 August 2003; Revised 7 October 2003

Copyright © 2004 S. Kalabušić and M. R. S. Kulenović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the rate of convergence of solutions of some special cases of the equation xn+1=(α+βxn+γxn1)/(A+Bxn+Cxn1), n=0,1,, with positive parameters and nonnegative initial conditions. We give precise results about the rate of convergence of the solutions that converge to the equilibrium or period-two solution by using Poincaré's theorem and an improvement of Perron's theorem.