基于子系统视角的复杂系统关联模式

Correlation Patterns for a Complex System from Its Sub-Systems’ Perspectives

摘要: 本文提出一种基于主体视角的复杂系统关系模式分析框架。首先，引入“主体肖像”概念，通过最大化参照主体与其他主体变量集的皮尔逊交叉相关系数绝对值，构建各主体对参照主体的映射关系。将该方法应用于全球金融系统，选取7个主要股票市场(富时A50指数、恒生指数、日经225指数、道琼斯工业平均指数、德国DAX30指数、法国CAC40指数和英国富时100指数)作为研究对象。研究发现：(1) 从恒生指数视角看，2020年后主导关系模式集中于金融、能源和旅游行业成分股，而2020年前则分散于全行业；(2) 考察了每个股票市场的映射，发现2020年前后关系模式存在共同主干(欧美与亚洲市场分别形成集群)，但也呈现显著差异。本框架为复杂系统关联结构研究提供了新思路，可推广至生理系统、生态系统等领域分析。

Abstract: This study develops an agent-centric framework for analyzing relational patterns in complex systems through subjective perspectives. The methodology introduces the innovative concept of “agent portraits”, constructed by maximizing absolute Pearson cross-correlation coefficients between linear combinations of a reference agent’s variables and those of other system components. Applied to global financial markets via seven major indices—FTSE China A50, Hang Seng, Nikkei 225, Dow Jones Industrial Average, DAX 30, CAC 40, and FTSE 100—the analysis reveals two critical findings: First, the Hang Seng Index perspective shows post-2020 dominance concentrated in financial, energy, and tourism sectors (pre-2020: dispersed across all industries); Second, the study examined the mapping of each stock market and found that while the relational patterns before and after 2020 share a common framework (with European-American and Asian markets forming distinct clusters), they also exhibit significant differences. This framework advances complex systems research by enabling perspective-dependent structural analysis, with demonstrated applicability to physiological networks and ecological systems through its scalable architecture for quantifying agent-specific interactions and dynamic pattern evolution.