| 摘要: |
| 引入双边无穷符号向量空间，从符号动力学的角度研究添加少数记忆函数后的基本细胞自动机规则40的动力学行为.借助计算机编程，找到了一个具有Bernoulli右移位性质的子系统，通过分析2阶有限型子移位对应的转移矩阵的性质，讨论其在子系统上的拓扑混合性和拓扑熵，进一步证明了它在这个子系统上同时具有Li－Yorke和Devaney意义下的混沌.该方法同样适用于其他细胞自动机的研究. |
| 关键词: 记忆细胞自动机 Bernoulli移位 混沌 |
| DOI： |
| 分类号: |
| 基金项目: |
|
| The Symbolic Dynamical Properties of Elementary Cellular Automata Rule 40 with Memory |
|
WANG Fang1， GUAN Jun biao2
|
| Abstract: |
| By introducing the bi infinite symbol vector space， the dynamical properties of elementary cellular automata rule 40 with minority memory are in depth studied from the symbolic dynamics perspective. Using computer programming， we get a subsystem with Bernoulli right shift. Then topological mixture and topological entropy on the subsystem are analyzed by the transition matrix， which is determined by the two order subshift of finite type. Furthermore， we indicate that it is chaotic in the sense of both Li Yorke and Devaney on the subsystem. Finally， the method presented in this paper is also applicable to other cellular automata. |
| Key words: elementary cellular automata with memory Bernoulli shift chaos |
