In this paper, we study the dynamical behaviors of neutral differential equations with small delays. We first establish the existence and smoothness of the global inertial manifolds for these equations. Then we further prove the smoothness of inertial manifolds with respect to small delays for a certain class of neutral differential equations. The method can be also applied to deal with more general small-delay systems. Finally, we apply our main results to the van der Pol oscillator model with small delay.

中文翻译：

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中立型时滞微分方程的光滑惯性流形。

在本文中，我们研究了具有小延迟的中立型微分方程的动力学行为。我们首先建立这些方程的整体惯性流形的存在性和光滑度。然后，对于一类中立型微分方程，我们进一步证明了惯性流形相对于小延迟的光滑性。该方法还可以应用于处理更通用的小延迟系统。最后，我们将主要结果应用于延迟较小的范德波尔振荡器模型。