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oai:www.ideals.illinois.edu:2142/88189 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

DeVille, Lee Rapti, Zoi Kirkpatrick, Kay L Zharnitsky, Vadim Berning, Stephen R 2015-09-29T20:49:56Z 2015-09-29T20:49:56Z 2017-09-30T09:15:18Z 2015-08 2015-07-16 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. Submission published under a 24 month embargo labeled 'U of I only', the embargo will last until 2017-08-01 2015-8 The student, Stephen Berning, accepted the attached license on 2015-07-15 at 01:11. The student, Stephen Berning, submitted this Dissertation for approval on 2015-07-15 at 01:27. This Dissertation was approved for publication on 2015-07-16 at 13:11. DSpace SAF Submission Ingestion Package generated from Vireo submission #8443 on 2015-09-29 at 14:59:30 Made available in DSpace on 2015-09-29T20:49:56Z (GMT). No. of bitstreams: 2 BERNING-DISSERTATION-2015.pdf: 1635741 bytes, checksum: da1fdb31589b35b5e007f82c475a8d3f (MD5) LICENSE.txt: 4212 bytes, checksum: 0012e51ab1906fe2020270b5f192ac22 (MD5) Previous issue date: 2015-07-16 Embargo set by: Seth Robbins for item 89469 Lift date: 2017-09-29T20:50:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 89469 on 2017-09-30T09:15:18Z. application/pdf http://hdl.handle.net/2142/88189 en Copyright 2015 Stephen Berning neural network neuronal network inhibitory neurons inhibition non-monotonic synchrony mean-field analysis integrate-and-fire limit theorem Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.