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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Berning, Stephen R

Contributors dc:contributor

• DeVille, Lee
• Rapti, Zoi
• Kirkpatrick, Kay L
• Zharnitsky, Vadim

• neural network
• neuronal network
• inhibitory neurons
• inhibition
• non-monotonic
• synchrony
• mean-field analysis
• integrate-and-fire
• limit theorem

Statement dc:rights

• Copyright 2015 Stephen Berning

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/88189