# Nonlinear dynamics of networks: the groupoid formalism

@article{Golubitsky2006NonlinearDO, title={Nonlinear dynamics of networks: the groupoid formalism}, author={Martin Golubitsky and I. N. Stewart}, journal={Bulletin of the American Mathematical Society}, year={2006}, volume={43}, pages={305-364} }

A formal theory of symmetries of networks of coupled dynamical
systems, stated in terms of the group of permutations of the nodes that preserve
the network topology, has existed for some time. Global network symmetries
impose strong constraints on the corresponding dynamical systems,
which affect equilibria, periodic states, heteroclinic cycles, and even chaotic
states. In particular, the symmetries of the network can lead to synchrony,
phase relations, resonances, and synchronous or…

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