复杂系统的演化过程,n(n-1)律,自聚集

研究一类复杂系统的演化过程,给出一个网络模型,由此导出f(n)=n(n-1),用以在某种程度上定性地描写演化过程中聚集与功能变化的规律。这里n表示agents的聚集数量。熟知的关系式1+1>2是n=2时的特例。当n为小数时,n的增减对系统整体功能的影响显著,此情况将称为“小n机制”。当n充分大时,系统的整体功能将有大跃升,并可用n2度量,称此为“n2效应”。一般情况下,n(n-1)描写聚集-相互作用-功能跃升的模式,用此模式可对不同领域的演化过程作某种解释。

The Evolving Processes of Complex Systems, Rule of n(n-1), Self-Clustering

In this paper,the evolving processes of one kind of complex systems are investigated.A network model is given,and f(n)=n(n-1) is derived where n is the clustering quantity of agents.It may be used,to some extent,to describe qualitatively the rules between clustering quantity n and the leap increase of system function in evolving process.The well-known representation 1+1>2 is the special case of n=2.When n is a small number, the fluctuation of n influences the change of the whole system function notably.This may be called "small n mechanism".When n is a sufficient large number,the whole system function will have a large leap increase and it may be measured by n~2.This case may be called "n~2-effect".In general,n(n-1) describes the pattern: clustering-interacting-leap increasing of function,by which,to a certain extent,the evolving processes in different domains may be explained.