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.[1] In the following, everything is implicitly assumed to be finite unless stated otherwise.
^Wu, Chai Wah (2005). "Synchronization in networks of nonlinear dynamical systems coupled via a directed graph". Nonlinearity. 18 (3): 1057–1064. Bibcode:2005Nonli..18.1057W. doi:10.1088/0951-7715/18/3/007. S2CID 122111995.
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