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

Yao Li, Logan Chariker, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
JournalJournal of Mathematical Biology
DOIs
StateAccepted/In press - Jan 1 2018

Fingerprint

Membrane Potential
Reduced Model
dynamic models
Network Model
Neurons
Neuron
neurons
Membrane Potentials
Nonequilibrium Steady State
Simple Random Walk
First Passage Time
membrane potential
Membranes
Discrepancy
Stochastic Model
Existence and Uniqueness
Control nonlinearities
Synchronization
Nonlinearity
Stochastic models

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

How well do reduced models capture the dynamics in models of interacting neurons? / Li, Yao; Chariker, Logan; Young, Lai-Sang.

In: Journal of Mathematical Biology, 01.01.2018.

Research output: Contribution to journalArticle

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