Open AccessGlobal attractor of coupled difference equations and applications to Lotka-Volterra systems
Author(s) -
C. V. Pao
Publication year - 2005
Publication title -
advances in difference equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.67
H-Index - 51
eISSN - 1687-1847
pISSN - 1687-1839
DOI - 10.1155/ade.2005.57
Subject(s) - mathematics , attractor , uniqueness , verifiable secret sharing , nonlinear system , ordinary differential equation , partial differential equation , constant (computer programming) , differential equation , mathematical analysis , computer science , physics , set (abstract data type) , quantum mechanics , programming language
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