Properties of solutions to one class of systems of ordinary differential equation of high dimension

A class of systems of high dimensional nonlinear ordinary differ\-en\-tial equations is considered. Asymptotic properties of solutions to these systems are investigated as the dimension increases. We prove that, for a sufficiently large number of equations, the last component of the solution to the Cauchy problem is an approximate solution to the initial-value problem for a delay differential equation.

УДК 517.925.54

Keywords: high dimensional system of ordinary differential equations, asymptotic properties of solutions, delay differential equation, limit theorem