抽象代数理论下的复杂系统模型

Complex System Model Based on the Theory of Abstract Algebra

复杂系统模型已经广泛地应用于生态学、中医学、物理、化学及其他学科.运用抽象代数理论对复杂系统模型进行了研究.首先对张应山所给出的有关复杂系统模型及其3种关系(等价关系、跃迁关系和返祖关系)的定义进行了阐述,然后在抽象代数理论的基础上给出几个引理并进行了证明,最后给出了复杂系统模型的一个等价定义.

The complex system model is widely used in ecology,traditional chinese medicine,physics,chemistry and other subjects.The complex system model was studied by using the theory of abstract algebra.Firstly,the definition of the complex system model and three relations（equivalent relation,transition relation and atavism relation） given by Zhang Yingshan was introduced.Secondly,some lemmas were given and proved on the basis of abstract algebra.Finally,an equivalent definition of the complex system model was given.