Hierarchical structure and multi time-scale in large scale dynamical systems

In this paper, we deal with approximation methods of large-scale systems which describe the macroscopic behavior of the whole system and simultaneously the partially microscopic one of the objective subsystems. We propose a hierarchical representation of such large-scale systems by employing the connection graph structure of the elements and multiple time-scale dynamics. The approximation accuracy is rigorously induced and numerical simulation is also demonstrated to show the efficiency.