Advances in Difference Equations
Volume 2005 (2005), Issue 1, Pages 57-79
doi:10.1155/ADE.2005.57
Global attractor of coupled difference equations and applications to Lotka-Volterra systems
Department of Mathematics, North Carolina State University, Raleigh 27695, NC, USA
Received 22 April 2004
Copyright © 2005 C. V. Pao. 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
This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive
solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.