基于Kolmogorov熵的系统协同效应度量方法及实证

Measurement and Empirical Research of Synergy in Complex Systems Based on Kolmogorov Entropy

度量协同度是协同学研究的核心和难点。通过分析现有协同度模型及其使用条件,发现基于协调发展思想的协同度模型在实际应用时有严格的限制条件,极大限制了其适用范围。基于协同效应思想,验证了Kolmogorov熵与系统协同度的关系,并构建了基于k熵的复杂系统协同度模型及量化方法。该方法考虑了序参量在系统某一时刻的发展趋势,能够在更大程度上反映系统的有序程度,弥补了现有研究的不足。最后,以中国2004~2015年各省份的科技金融系统为评价对象,对新的协同度模型与评价方法的应用范围进行了实证研究。分析发现,本模型不仅能够有效找到子系统的序参量,而且可以方便的计算系统协同度并以此描述系统发展对重大事件的反映。

It is a great challenge to measure the degree of synergy in complex systems.By investigating some models that focus on analyzing the degree of coordination,it has been found that most of them suffer strict constraints in the real applications.Based on synergetic effect ideology,in this article,we first explore and verify the relationship between Kolmogorov entropy and system synergy,and then propose a new model to quantify the degree of synergy in complex systems.Based on the trend of order parameter at some point in the system,the proposed model can be used to measure the degree of order in complex systems efficiently.The proposed model is on the base of the classical synergy theory,which opens a new research area and makes up the deficiency of existing research.By analyzing the synergetic degree of Science and Technology Financial System in each province of China from 2004 to 2015,we find that the proposed model can be used to find the ordering parameter of subsystem,calculating the system synergy,and describing the reflection of system development on important events,efficiently.