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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 38, Pages 2401-2413
http://dx.doi.org/10.1155/S0161171203210231

Existence and global stability of positive periodic solutions of a discrete delay competition system

1Department of Applied Mathematics, Gansu University of Technology, Lanzhou, Gansu 730050, China
2Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, China

Received 15 October 2002

Copyright © 2003 Hindawi Publishing Corporation. 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.

Abstract

The existence and the global stability of positive periodic solutions of a discrete competition model is studied. The model incorporates time delays and allows for a fluctuating environment. By means of some standard procedures of the topological degree method and the construction of a suitable Lyapunov function, sufficient conditions are obtained to ensure the existence and the global stability of positive periodic solutions of the above systems.