系统科学与数学  2011, Vol. 31 Issue (9): 1045-1051    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 |

THE SELF-CLUSTERING IN COMPLEX SYSTEMS, FUNCTION OF SYSTEMS AND POSITIVE FEEDBACK
ZHANG  Si-Ying
School of Information Science and Engineering, Northeastern University, Shenyang 110004; Institute of Complexity Science, Qingdao University, Qingdao
 全文: PDF (569 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料

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 $f(n)=\frac{1}{2}n(n-1)$ 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.
 [1] 黄捷. 输出调节问题综述[J]. 系统科学与数学, 2011, 31(9): 1055-1081. [2] 黄一, 薛文超. 自抗扰控制纵横谈[J]. 系统科学与数学, 2011, 31(9): 1111-1129. [3] 张强, 张纪峰. 基于马尔科夫拓扑切换和随机通信干扰的连续时间多自主体系统的趋同控制[J]. 系统科学与数学, 2011, 31(9): 1097-1110. [4] 张戌希, 程代展. 一类非最小相位非线性系统的鲁棒输出调节[J]. 系统科学与数学, 2011, 31(9): 1082-1091. [5] 赵千川. 添加捷径对环状DEDS的影响分析[J]. 系统科学与数学, 2011, 31(9): 1092-1096. [6] 王峰, 孙经先, 崔玉军. 零点指数的计算及其对二阶周期边值问题的应用[J]. 系统科学与数学, 2011, 31(8): 975-984. [7] 汪忠志, 杨卫国. 关于相依离散随机序列的若干强偏差定理[J]. 系统科学与数学, 2011, 31(8): 932-942. [8] 王子亭, 梁月, 王晓洁. 奇异Hamilton-Jacobi-Bellman 方程粘性解的存在唯一性[J]. 系统科学与数学, 2011, 31(8): 1000-1009. [9] 关杰, 丁林, 张应杰. $(X + K)\bmod 2^n$运算和$X \oplus K$运算异或差值的概率分析及其应用[J]. 系统科学与数学, 2011, 31(8): 952-960. [10] 叶盼盼, 杨志林. 二阶常微分方程组积分边值问题的正解[J]. 系统科学与数学, 2011, 31(8): 992-999. [11] 张鹏. 连续型凸动态规划的离散近似迭代法研究[J]. 系统科学与数学, 2011, 31(8): 943-951. [12] 陈金梅, 王祥. 一类非线性波动方程弱解的存在唯一性[J]. 系统科学与数学, 2011, 31(8): 985-991. [13] 张恩瑜, 王珏, 汪寿阳. 一种新的Vague集多准则决策评分函数[J]. 系统科学与数学, 2011, 31(8): 961-974. [14] 谷峰. 有限个平衡问题与非扩张映象不动点问题的复合迭代方法[J]. 系统科学与数学, 2011, 31(7): 859-871. [15] 王艳萍, 陈志平, 陈玉娜. 因子结构下的新型多期投资组合选择模型[J]. 系统科学与数学, 2011, 31(7): 824-836.