We consider some system of ordinary differential equations modeling a multistage synthesis of a substance. We prove the global limit theorems that establish connections between the solutions to a system of ordinary differential equations of large dimension and the solutions to a delay equation. The obtained results enable us to find the approximate solutions to the systems under consideration of an arbitrarily high dimension on the whole half-axis. Some approximation estimates are established.

中文翻译：

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关于一类大维常微分方程和时滞方程

我们考虑一些常态微分方程系统，该系统对物质的多级合成进行建模。我们证明了全局极限定理，该全局极限定理在一个大维常微分方程组的解与一个延迟方程的解之间建立了联系。所获得的结果使我们能够找到在整个半轴上任意大尺寸考虑下的系统的近似解。建立一些近似估计。