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

doi:10.13438/j.cnki.jdzk.2026.02.005

Abstract

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

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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