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

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

Hai-Feng Huo1 and Wan-Tong Li2

 1Department of Applied Mathematics, Gansu University of Technology, Lanzhou 730050, Gansu, China
2Department of Mathematics, Lanzhou University, Lanzhou 730000, Gansu, China
Received 15 October 2002

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.