  This paper studies, in fine details, the long-time asymptotic behavior of
decaying solutions of a general class of dissipative systems of nonlinear
differential equations in complex Euclidean spaces. The forcing functions
decay, as time tends to infinity, in a coherent way expressed by combinations
of the exponential, power, logarithmic and iterated logarithmic functions. The
decay may contain sinusoidal oscillations not only in time but also in the
logarithm and iterated logarithm of time. It is proved that the decaying
solutions admit corresponding asymptotic expansions, which can be constructed
concretely. In the case of the real Euclidean spaces, the real-valued decaying
solutions are proved to admit real-valued asymptotic expansions. Our results
unite and extend the theory investigated in many previous works.
