易的结构演化及其数学基础和发展,生态及系统的生克模型

Evolvement of Structures on Yi and Their Mathematical Bases and Developments,and the Promotion-Restriction Model of Ecology and System Theory

首先讨论了从易到五行、太玄、太极图等的结构演化及相应的数学基础。其次探讨了易学的某些可能的数学发展,如复变函数、信息、统计、对称群、线性代数、符号动力学、非线性方程和高维空间等。第三探索了易生物学的若干方面和生物对易学的启示。第四简化生态系统中各种生物之间的关系为生克二种,而得到生态系统的生克模型,并由相应的二元方程组的定性分析方法可以描述生物多样性。最后,由此推广为社会及一般系统的生克模型;并简要介绍与易密切相关的东方经济学。

First, we discuss the evolvement of structures from Yi to Five-Element, Tai-Xuan, Tai-Ji Figure, etc., and corresponding mathematical bases. Next, we research some possible mathematical developments, for example, complex analysis, information, statistics, symmetric group, linear algebra, symbolic dynamics, nonlinear equations, and high-dimensional space, etc. Thirdly, some aspects on the Yi-biology and enlightenment for Yi from biology are searched. Fourthly, the relations among various living are simplified to promotion or restriction in an ecological system, and derive a promotion-restriction model of the ecological system, and then the biological variety is described by the methods of qualitative analysis of nonlinear equation sets. Finally, it is extended to the promotion-restriction model of society and general system, and the east （oriental） economics related closely with Yi is briefly introduced.