Global attractor of coupled difference equations and applications to Lotka-Volterra systems
Advances in Difference Equations volume 2005, Article number: 471586 (2005)
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.
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Pao, C.V. Global attractor of coupled difference equations and applications to Lotka-Volterra systems. Adv Differ Equ 2005, 471586 (2005). https://doi.org/10.1155/ADE.2005.57