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

C. V. Pao | Zendy

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Global 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

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