细胞自动机传播现象的拓扑动力学研究

项目名称： 细胞自动机传播现象的拓扑动力学研究

项目编号： No.11301122

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 管俊彪

作者单位： 杭州电子科技大学

项目金额： 22万元

中文摘要： 广泛应用于复杂系统模拟的细胞自动机(特别是普适细胞自动机)在时空演化过程中多出现传播现象，然而目前对于产生这种现象的机理数学上尚无明确的解释。本项目旨从拓扑动力学角度重点揭示初等细胞自动机传播动力学行为，探索普适细胞自动机的部分普适特性，建立一般符号动力学意义下细胞自动机的符号表示，拓展细胞自动机动力学及符号动力学的相关理论。本项目研究内容主要包括：初等细胞自动机中复杂伯努利移位规则及超伯努利移位规则传播动力学性质研究；普适初等细胞自动机规则部分普适特性研究；细胞自动机符号表示研究。本项目旨在从非线性动力学观点分析细胞自动机产生传播现象的机理，为建立在传播动力学上的计算及运用细胞自动机模拟复杂系统提供理论依据。

中文关键词： 细胞自动机；拓扑动力学；传播现象；符号表示；群体疏散

英文摘要： Cellular automata are widely used as simulation tools for modeling many complex systems, and they (especially universal cellular automata)often exhibit propagation phenomena during the spatio-temporal evolution process. However,so far there is lack of explicit explanation concerning such mechanism from mathematical point of view. This work is devoted to the investigation of the propagation dynamics of the elementary cellular automata, and the exploration of some universal features of the universal cellular automaton from the viewpoint of topological dynamics. Moreover, it aims to establish symbolic representations of cellular automata in the sense of general symbolic dynamics, and generalize some related theories of dynamics of cellular automata and symbolic dynamics. The main contents of this research include: the investigations of propagation dynamics of complex Bernoulli shift rules and hyper Bernoulli shift rules in the elementary cellular automata；the study of some universal features of the universal elementary cellular automaton；the discussions of symbolic representations of cellular automata. The purpose of this research is to analyze the mechanism of propagation dynamics of cellular automata from the nonlinear dynamics perspective, which may provide some theoretical foundations for the computation base

英文关键词： Cellular automaton；topological dynamics；propagation phenomenon；symbolic representation；crowd evacuation