有向根树上局部更新函数为NAND或NOR的广义并序动力系统的固定点  

Fixed Points in Generalized Parallel Dynamical System with NAND or NOR Local Functions over Directed Rooted Trees

作　　者：孙彦文 郑洁[1] SUN Yanwen;ZHENG Jie(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《Journal of Donghua University(English Edition)》2024年第2期214-220,共7页东华大学学报（英文版）

基　　金：2021 Shanghai Philosophy and Social Sciences Planning Project(No.2021BFX005)。

摘　　要：研究对象为有向根树上的广义并序动力系统,其局部更新函数为NAND或NOR。为了研究这类广义并序动力系统中的固定点的个数及状态,采用结构分析法和分类讨论法,得到了此类动力系统中关于固定点的确切结果。证明了这类广义并序动力系统中的固定点状态完全由有向根树中的自环决定。离散动力系统是数学建模的重要工具,该文可为离散动力系统的研究提供新的思路。In order to study the exact number and states of fixed points in the generalized dynamical system with NAND or NOR local functions over directed rooted trees,structural analysis and classification discussion methods are applied.The exact results of the fixed points in such dynamical systems are obtained.It is proved that the fixed points in such dynamical systems are completely determined by the loops in the rooted trees.This work provides a relevant advance in the knowledge of discrete dynamical systems which constitute mathematical tools to model simulation processes.

关 键 词：广义并序动力系统 有向根树 布尔函数 固定点 

分 类 号：O158[理学—数学] O29[理学—基础数学]