Approximating network dynamics: Some open problems

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© 2018 American Institute of Mathematical Sciences. All Rights Reserved. Discrete-time finite-state dynamical systems on networks are often conceived as tractable approximations to more detailed ODE-based models of natural systems. Here we review research on a class of such discrete models N that approximate certain ODE models M of mathematical neuroscience. In particular, we outline several open problems on the dynamics of the models N themselves, as well as on structural features of ODE models M that allow for the construction of discrete approximations N whose predictions will be consistent with those of M.