Copyright © 2013 Changjin Xu and Yusen Wu. 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.
A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained.