Is it possible to obtain the solution to a networked ode system according to the solutions to the subsystems?

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Given a networked ode system

$\frac{dx_i}{dt}=f(x_i)+\sum_{j=1}^N A_{ij} g(x_i,x_j),\forall i\in\{1,\dots,N\}$

I am wondering whether the solution to this system can be somehow aggregated from the solutions to the subsystems.