| The purpose of this talk is to investigate the dynamics of a nonlinear finite difference system which approximates a class of nonlinear reaction-diffusion equations with time delay. It is shown that for one class of initial vectors the solution u(n) of the finite difference system converges to the maximal solution of the corresponding "steady-state" problem, while for another class of initial vectors it converges to the minimal solution. When the maximal and minimal solutions coincide it yields a unique solution u * of the steady-state problem, and the solution u(n) converges to u * for every initial vector in a sector. A sufficient condition for the uniqueness of u * is given. The above convergence results are applied to a reaction-diffusion problem with three different types of reaction functions. |