完全二部图上XOR-OR 并行混合动力系统的固定点与周期点

doi:10.13438/j.cnki.jdzk.2026.02.005

吉首大学学报（自然科学版） ›› 2026, Vol. 47 ›› Issue (2): 24-33.DOI: 10.13438/j.cnki.jdzk.2026.02.005

完全二部图上XOR-OR 并行混合动力系统的固定点与周期点

薛雅婷，郑洁，李奇珂

（1.东华大学数学与统计学院，上海 201620；2.南安普顿大学语言文化语言学系，英国南安普顿 SO17 1BJ）

出版日期:2026-03-25 发布日期:2026-04-24

Fixed Points and Periodic Points in XOR-OR Parallel Hybrid Dynamical Systems over Complete Bipartite Graphs

XUE Yating,ZHENG Jie,LI Qike

(1.School of Mathematics and Statistics,Donghua University,Shanghai 201620,China; 2.Department of Languages Cultures Linguistics,University of Southampton,Southampton SO17 1BJ,UK)

Online:2026-03-25 Published:2026-04-24
Supported by:
"Smart Curriculum" Project of Donghua University (ZHH-2025-08);Shanghai Philosophy and Social Sciences Planning Project (2021BPX005)

摘要/Abstract

摘要：主要研究了完全二部图上，图的2个顶点子集分别配置为XOR和OR函数的并行混合动力系统的动态演化行为.结合数学推导与计算机模拟，根据配置OR函数顶点集合基数的奇偶性，分析了系统不动点与周期点的特性.研究结果表明，当OR函数顶点的数目为奇数时，系统同时存在固定点和周期为 2 的周期点；当OR函数顶点的数目为偶数时，系统仅存在固定点.进一步给出了上述2种情况下固定点和周期点存在的充要条件，并推导出精确的计数公式.

关键词： 并行混合动力系统, 完全二部图, 固定点, 周期点

Abstract: This paper investigates the dynamical evolution of parallel hybrid dynamical systems on complete bipartite graphs,where the local functions for the two vertex sets are configured as the Boolean XOR and OR functions,respectively.Through mathematical deduction and computer simulation,the results show that when the number of OR-vertices is odd,the system exhibits both fixed points and period-2 points.Conversely,when the number of OR-vertices is even,only fixed points exist.Furthermore,the necessary and sufficient conditions for the existence of these states,along with their specific counting formulas,are derived.

Key words: parallel hybrid dynamical system, complete bipartite graph, fixed point, periodic point

薛雅婷, 郑洁, 李奇珂. 完全二部图上XOR-OR 并行混合动力系统的固定点与周期点[J]. 吉首大学学报（自然科学版）, 2026, 47(2): 24-33.

XUE Yating, ZHENG Jie, LI Qike. Fixed Points and Periodic Points in XOR-OR Parallel Hybrid Dynamical Systems over Complete Bipartite Graphs[J]. Journal of Jishou University(Natural Sciences Edition), 2026, 47(2): 24-33.

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完全二部图上XOR-OR 并行混合动力系统的固定点与周期点

Fixed Points and Periodic Points in XOR-OR Parallel Hybrid Dynamical Systems over Complete Bipartite Graphs

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