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.
Iserles, A first course in the numerical analysis of differential equations , Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1996
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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.