复杂系统中的自聚集, 系统功能与正反馈

张嗣瀛

系统科学与数学 ›› 2011, Vol. 31 ›› Issue (9) : 1045-1051.

PDF(569 KB)
PDF(569 KB)
系统科学与数学 ›› 2011, Vol. 31 ›› Issue (9) : 1045-1051. DOI: 10.12341/jssms11687
论文

复杂系统中的自聚集, 系统功能与正反馈

    张嗣瀛
作者信息 +

THE SELF-CLUSTERING IN COMPLEX SYSTEMS, FUNCTION OF SYSTEMS AND POSITIVE FEEDBACK

     ZHANG  Si-Ying
Author information +
文章历史 +

摘要

提出了复杂系统中自聚集的概念, 这是广泛存在于复杂系统中的一种自组织的形式, 然后考虑系统的功能, 尝试对熟知的1+1>2(总体大于部分之和),
即关于系统功能的定性表达, 寻求一种进一步定量定性的更一般的关系.  给出了一个描述复杂系统的简单的网络模型, 它有相当广泛的代表性,
并用它分析系统的生长、演化及涌现过程以及在过程中功能的变化, 得到一个定量定性的关系式f(n)=12n(n1), 表达功能变化规律.
此式能揭示系统功能的一些性质并解释一些重要现象, 诸如: 1+1>2 是此式当n=2时的特例, 此式还给出具体的非线性;
它还说明系统生长初期, 组分的增减对系统的功能影响显著;当系统规模达到一定大时, 将导致稳态涌现;
以及系统功能从起始的脆弱性到稳态涌现的鲁棒性. f(n)还蕴涵着正反馈的激励放大机制, 并给出一个表达式.
据此说明此式可作为``报酬递增''的机制以及导致无标度网结构形成的``优先连接''的机制. 最后是几句关于复杂与简单的话.

Abstract

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 1+1>2 , 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 f(n)=12n(n1) for system function can be derived. This expression indicates properties of the system function and gives explanations of some important phenomena.  Such as: 1+1>2 is a special case of f(n) as n=2. Moreover, f(n) 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 n 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, f(n) 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.

关键词

复杂系统 /   / 自聚集 /   / 系统功能 /   / 复杂网络 /   / 正反馈

引用本文

导出引用
张嗣瀛. 复杂系统中的自聚集, 系统功能与正反馈. 系统科学与数学, 2011, 31(9): 1045-1051. https://doi.org/10.12341/jssms11687
ZHANG Si-Ying. 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
中图分类号: 93A15    93A30    94C99   
PDF(569 KB)

397

Accesses

0

Citation

Detail

段落导航
相关文章

/