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

Berning, Stephen R

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

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

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

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

Copyright and License Information

Copyright 2015 Stephen Berning

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