This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in (Ann Inst H Poincaré Anal Non Linéaire, 4(1):1–47 1987). We study the long-time dynamics of a large class of dissipative systems of nonlinear ordinary differential equations with time-decaying forcing functions. The nonlinear term can be, but not restricted to, any smooth vector field which, together with its first derivative, vanishes at the origin. The forcing function can be approximated, as time tends to infinity, by a series of functions which are coherent combinations of exponential, power and iterated logarithmic functions. We prove that any decaying solution admits an asymptotic expansion, as time tends to infinity, corresponding to the asymptotic structure of the forcing function. Moreover, these expansions can be generated by more than two base functions and go beyond the polynomial formulation imposed in previous work.

本文进一步和系统地发展了Foias和Saut在（Ann Inst HPoincaréAnal NonLinéaire，4（1）：1-47 1987）中提出的渐进扩张理论。我们研究了一类具有时滞强迫函数的非线性常微分方程耗散系统的长期动力学。非线性项可以是但不限于任何平滑矢量场，该矢量场及其一阶导数在原点消失。随着时间趋于无穷大，可以通过一系列函数来近似逼迫函数，这些函数是指数函数，幂函数和迭代对数函数的相关组合。我们证明，随着时间趋于无穷大，任何衰减解都允许渐进展开，这与强迫函数的渐近结构相对应。此外，