University of Illinois Urbana-Champaign

Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons

Berning, Stephen R

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BERNING-DISSERTATION-2015.pdf

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https://hdl.handle.net/2142/88189

Description

Title
Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons
Author(s)
Berning, Stephen R
Issue Date
2015-07-16
Director of Research (if dissertation) or Advisor (if thesis)
DeVille, Lee
Doctoral Committee Chair(s)
Rapti, Zoi
Committee Member(s)
  • Kirkpatrick, Kay L
  • Zharnitsky, Vadim
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2015-09-29T20:49:56Z
Keyword(s)
  • neural network
  • neuronal network
  • inhibitory neurons
  • inhibition
  • non-monotonic
  • synchrony
  • mean-field analysis
  • integrate-and-fire
  • limit theorem
Abstract
We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.
Graduation Semester
2015-8
Type of Resource
text
Permalink
http://hdl.handle.net/2142/88189
Copyright and License Information
Copyright 2015 Stephen Berning

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