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.
孙彦文;郑洁
东华大学 理学院,上海 201620
数学
广义并序动力系统;有向根树;布尔函数;固定点
generalized parallel dynamical system;directed rooted tree;Boolean function;fixed point
《东华大学学报（英文版）》 2024 (002)
214-220 / 7
2021 Shanghai Philosophy and Social Sciences Planning Project(No.2021BFX005)
10.19884/j.1672-5220.202309008
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