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In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties (e.g. the network connectivity) and the global dynamics that result. The work on GDSs considers finite graphs and finite state spaces. As such, the research typically involves techniques from, e.g., graph theory, combinatorics, algebra, and dynamical systems rather than differential geometry. In principle, one could define and study GDSs over an infinite graph (e.g. cellular automata or probabilistic cellular automata over or interacting particle systems when some randomness is included), as well as GDSs with infinite state space (e.g. as in coupled map lattices); see, for example, Wu. In the following, everything is implicitly assumed to be finite unless stated otherwise. ==Formal definition== A graph dynamical system is constructed from the following components:
The ''phase space'' associated to a dynamical system with map ''F'': ''Kn → Kn'' is the finite directed graph with vertex set ''Kn'' and directed edges (''x'', ''F''(''x'')). The structure of the phase space is governed by the properties of the graph ''Y'', the vertex functions (''fi'')''i'', and the update scheme. The research in this area seeks to infer phase space properties based on the structure of the system constituents. The analysis has a local-to-global character. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Graph dynamical system」の詳細全文を読む スポンサード リンク
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