Open Access

Global attractor of coupled difference equations and applications to Lotka-Volterra systems

Advances in Difference Equations20052005:471586

DOI: 10.1155/ADE.2005.57

Received: 22 April 2004

Published: 14 March 2005

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.

Authors’ Affiliations

(1)
Department of Mathematics, North Carolina State University

Copyright

© Pao 2005