Runge-Kutta discretization commutes with every affine map that relates two vector fields, so affine invariant submanifolds such as synchrony polydiagonals are preserved in the discrete dynamics.
Brown, Near Algebras, PhD thesis, Ohio State Univ., 1966
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Runge-Kutta and Networks
Runge-Kutta discretization commutes with every affine map that relates two vector fields, so affine invariant submanifolds such as synchrony polydiagonals are preserved in the discrete dynamics.