Global attractor of a coupled finite difference reaction diffusion system with delays. (English) Zbl 1048.35010

This paper is devoted to investigation of the asymptotic behaviour of solutions for a coupled finite difference system which is a discrete approximation of a class of time-delayed reaction diffusion system of two equations under Neumann boundary condition. Using the backward Euler approximation for this system, the author shows the existence and uniqueness of positive global solution of the finite difference system. In order to investigate the global attraction of the time-dependent solution, the existence of constant positive solutions for the steady-state problem is showed, first.
Sufficient conditions are given to ensure the global attraction of a positive steady-state solution for each of the three types of quasimonotone reaction functions: cooperative, competition and prey-predator.
These global attraction results are applied to three Lotka-Volterra models.


35B41 Attractors
35K57 Reaction-diffusion equations
39A11 Stability of difference equations (MSC2000)
Full Text: DOI


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