摘要
研究复杂系统要探索整体规律。本文指出:为此,需要对定性研究予以适当重视。文中给出一个表达式(E):Sni=11i=E(n),即自聚集、自组织,演化发展到新层次。此式用以描述复杂系统的结构形成及动态行为。还对其中“自聚集”的概念给以着重阐述。又分析了聚集的量对系统功能的影响,并给出表达式(C):11+12+…+1n>en2。然后,从生物、自然界、社会、工程等不同领域,解释可用(E)式概括的一些规律性现象;还从复杂系统的观点并借助(E)式讨论了对“从量变到质变”的进一步认识。最后,将复杂系统的自相似结构与分形自相似结构对比,指出一类复杂系统其结构的形成实质是由简单规则多次重复而来,即复杂寓于简单,且聚集、组织,再聚集、再组织……即(E)式多次重复,是形成一类复杂系统结构的基本规则。
For complex systems, rules of the whole systems should be investigated. Consequently, appropriate attention should pay to the qualitative researches. In this paper, a representation （E） ： S（∑i=1^n 1i） = E（n） is given. It means： self-clustering, self-organizing and evolving to a new level. （E） is used to describe the formation of the structures of complex systems and their dynamic behavior. The concept ＇ self-clustering＇ is explained. The effect of clustering quantity to system ability is analyzed. Another representation （C） ：11 ＋ 12 ＋ …… ＋ 1n 〉 en^2 is followed. Many examples in different domains, such as in biology, natural world, social science, economics, engineering, etc, are given which can be explained by （E）. From the standpoint of complex systems and with the aid of （E） , the understanding of from quantitative change to qualitative change＇ is discussed. Finally, by comparing the self-similarity in the structures of complex systems with that in fractal, we can see that the complex structures are formed by repeating some simple rule again and again, so complexity is besides in simplicity. Moreover, self-clustering, self-organizing and repeating is the basic rule to form the structures of a kind of complex systems.
出处
《复杂系统与复杂性科学》
EI
CSCD
2005年第1期71-83,共13页
Complex Systems and Complexity Science
关键词
整体规律与定性研究
自聚集
结构形成与动态行为
自相似性
涌现
rules of whole system and qualitative researches
self-clustering
formation of structures and dynamic behavior
self-similarity
emergence
