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Wilson-Cowan Equations for Neocortical Dynamics.

Jack D Cowan1, Jeremy Neuman2, Wim van Drongelen3

  • 1Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL, 60637, USA. cowan@math.uchicago.edu.

Journal of Mathematical Neuroscience
|January 6, 2016
PubMed
Summary
This summary is machine-generated.

The Wilson-Cowan and Markov models quantitatively explain neocortical activity, including spontaneous firing patterns and responses to stimuli. These models reveal distinct modes of cortical responses, differentiating between low and high intensity stimulations.

Keywords:
Bogdanov–Takens bifurcationDirected percolation phase transitionLocalized decaying LFP and VSD responsesNeural network master equationPair-correlationsPropagating decaying LFP and VSD wavesWilson–Cowan equations

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Area of Science:

  • Computational Neuroscience
  • Mathematical Biology
  • Systems Neuroscience

Background:

  • The Wilson and Cowan model (1972-1973) described neocortical neuron population dynamics but excluded fluctuations.
  • Later Markov models (Ohira & Cowan, Buice & Cowan) incorporated fluctuation and correlation effects.

Purpose of the Study:

  • To demonstrate how both Wilson-Cowan and Markov models quantitatively explain neocortical activity.
  • To analyze spontaneous activity, power spectra, and pair correlations.
  • To explain distinct cortical response modes to stimuli.

Main Methods:

  • Utilized Markov models to analyze spontaneous neocortical activity and its power spectrum.
  • Applied models to explain pair correlations in resting and stimulated cortex.
  • Employed Wilson-Cowan equations to model distinct cortical response modes.

Main Results:

  • Markov models accurately describe spontaneous neocortical activity, including Brownian motion baselines and directed percolation in spiking bursts.
  • Models explain slow decay of pair correlations in resting cortex and rapid decay in stimulated cortex.
  • Wilson-Cowan equations account for two distinct cortical response modes: propagating waves and localized responses.

Conclusions:

  • Both Wilson-Cowan and Markov models provide quantitative accounts of neocortical population dynamics.
  • The models successfully explain spontaneous activity, correlations, and stimulus-evoked responses.
  • Neocortical activity exhibits complex behaviors, including distinct response modes, that can be mathematically modeled.