完全二部图上XOR-OR并行混合动力系统的固定点与周期点OA
Fixed Points and Periodic Points in XOR-OR Parallel Hybrid Dynamical Systems over Complete Bipartite Graphs
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.
This paper investigates the dynamical evolution of parallel hybrid dynamical systems on com-plete 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 re-sults 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 for-mulas,are derived.
薛雅婷;郑洁;李奇珂
东华大学数学与统计学院,上海 201620东华大学数学与统计学院,上海 201620南安普顿大学语言文化语言学系,英国 南安普顿 SO17 1BJ
数理科学
并行混合动力系统完全二部图固定点周期点
parallel hybrid dynamical systemcomplete bipartite graphfixed pointperiodic point
《吉首大学学报（自然科学版）》 2026 (2)
24-33,10
"Smart Curriculum"Project of Donghua University(ZHH-2025-08)Shanghai Philosophy and So-cial Sciences Planning Project(2021BPX005)
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