# American Institute of Mathematical Sciences

July  2018, 23(5): 1917-1930. doi: 10.3934/dcdsb.2018188

## Approximating network dynamics: Some open problems

 Department of Mathematics, Ohio University, Athens, OH 45701, USA

Received  April 2017 Revised  June 2017 Published  May 2018

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 $M$.

Citation: Winfried Just. Approximating network dynamics: Some open problems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1917-1930. doi: 10.3934/dcdsb.2018188
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