How well do reduced models capture the dynamics in models of interacting neurons?

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced...

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Bibliographic Details
Published in:Journal of mathematical biology 2019-01, Vol.78 (1-2), p.83-115
Main Authors: Li, Yao, Chariker, Logan, Young, Lai-Sang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer simulation
Cortex
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Neurons
Random walk
Random walk theory
Stochastic models
Stochasticity
Synchronism
Synchronization
Variations
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Summary:This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with “nonlinearities” in the time evolution of membrane potentials. The use of simple random walks and their first passage times to simulate fluctuations in neuronal membrane potentials and interspike times is also considered.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-018-1268-0