This article is cited in 8 papers

On the properties of solutions to a class of nonlinear systems of differential equations of large dimension

I. I. Matveeva^ab, I. A. Mel'nik<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Abstract: We consider the Cauchy problem for a class of nonlinear systems of differential equations of large dimension, establish some properties of solutions, and prove that for a sufficiently large number of differential equations the last component of the solution is an approximate solution to the initial value problem for a delay differential equation.

Keywords: system of ordinary differential equations of large dimension, limit theorems, delay differential equation.

UDC: 517.925.5+517.929

Received: 21.03.2011

 English version: Siberian Mathematical Journal, 2012, 53:2, 248–258

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