In this paper the concept of ``self-clustering" is presented. It is one kind of the self-organizing and widely existing in complex systems. For the function of complex systems, there is a well-known inequality , showing that the whole is more than the sum of its parts. Could it seek one more quantitative expression for the function of complex systems? For this purpose a simple but widely representative network model is given. With this model, the process of growing, evolving and emergence of the system can be analyzed and a quantitative/qualitative expression for system function can be derived. This expression indicates properties of the system function and gives explanations of some important phenomena. Such as: is a special case of as . Moreover, shows the nonlinearity obviously. It also shows that at the initial stage of the process, adding or losing a few components will give rise to notable effect to the system function. There will be a steady emergence as increased to a considerable amount.
Thus, it reveals the change that from the fragility at the initial stage to the robustness accompanying the steady emergence. In addition, implies positive feedback. An expression is given to show this mechanism, which turns out to be the mechanism of "increasing returns" and the mechanism of ``preferential attachment", leading to the scale-free network structure. Finally, a brief conclusion regarding complexity and simplicity is given.
ZHANG Si-Ying. , {{custom_author.name_en}}.
THE SELF-CLUSTERING IN COMPLEX SYSTEMS, FUNCTION OF SYSTEMS AND POSITIVE FEEDBACK. Journal of Systems Science and Mathematical Sciences, 2011, 31(9): 1045-1051 https://doi.org/10.12341/jssms11687