ORDINARY DIFFERENTIAL EQUATIONS On the Relationship Between Solutions of Delay Differential Equations and Infinite-Dimensional Systems of Differential Equations

Abstract—We study the limit properties of solutions for a class of systems of ordinary differen-tial equations as the number of equations and a certain parameter grow unboundedly. We show that the sequence of functions formed by the last components of solutions of such systems has a repeated limit. The limit function is a solution of a delay differential equation. Estimates of the convergence rate are obtained. DOI: 10.1134/S0012266109010042 1