混沌边缘的区间定位与动力机制——以黄金分割轴为分析框架

Study on Interval Mapping and Dynamic Mechanism of Edge of Chaos——Taking Golden Mean as Analysis Framework

从1963年洛伦兹提出混沌理论,到1985年圣菲研究所朗顿提出混沌的边缘,混沌理论一次次引起科学界的兴趣。混沌边缘在哪儿?专家们惟妙惟肖的描述难以消除人们的疑惑,对混沌边缘的定位和运行机理的研究,成为混沌理论难以绕开的难题。本文试图说明黄金分割与混沌边缘之间具有深层的内在联系,黄金分割是许多复杂机体内在尺度选择的比例关系,通过混沌边缘在黄金分割轴上的尺度定位,为混沌边缘找到了量化的比例关系,并且通过对混沌边缘动力机制的分析和梳理,进一步深化了对混沌理论及相关复杂性范畴的理解和解释。

From lorentz’s chaos theory in 1963 to langton’s chaos theory in 1985,chaos theory has attracted the interest of the scientific community.Where is the edge of chaos?It is difficult for experts to eliminate people’s doubts with their vivid description.The research on the location and operation mechanism of chaos edge becomes a difficult problem for chaos theory to get around.This paper tries to illustrate deep inner connection between the golden mean and the edge of chaos.Golden mean is the proportion relation of inner scale selection of many complex body.By the scale of the edge of chaos on the golden shaft positioning,it found the proportion of quantitative relations for edge of chaos.Through the analysis of the edge of chaos dynamic mechanism,it further deepenes the understanding of the complexity of chaos theory and related category and explanation.