Abstract: There are various complex systems in nature, for instance turbulence and organism. In the present stage, the lack of effective methodologies and ideas hinders the further understanding of these challenging problems, e.g., the multi-scale and nonlinear behaviors of complex systems. As a promising direction to develop novel analyses approaches, the structure characterization can be regarded as a reasonable extension of the classical geometry analysis from simple to complex systems. In this paper, the general goals and ideas of the approaches to be developed were expounded. Moreover, based on the achieved results, some tentative guidelines and prerequisites were suggested for structure characterization.

Key words: complex system; structure characterization; multi-scale; nonlinearity