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Collective dynamics and self-organisation of stochastic neuronal systems influenced by synaptic time delay

Kolektivna dinamika i samoorganizacija stohastičkih neuronskih sistema pod uticajem sinaptičkog kašnjenja.

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2013
Disertacija4309.pdf (6.691Mb)
Author
Franović, Igor T.
Mentor
Burić, Nikola
Committee members
Radović, Zoran
Knežević, Milan
Elezović-Hadžić, Sunčica
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Abstract
The focus in the present thesis lies with the synchronization mediated self-organization phenomena in populations of globally coupled stochastic excitable or bursting units subjected to interaction delays. Excitable local dynamics follows the Fitzhugh- Nagumo model, canonical for type II excitability, whereas the bursting units are represented by the Hindmarsh-Rose model. The study comprises two complementary lines of research. One is aimed at extending the analogy regarding the complex forms of collective behavior exhibited by the assemblies of coupled nonlinear autonomous oscillators and those made up of excitable units. Within the second line of research, our main contribution consists in developing the mean-field based models for the collective dynamics of the assemblies of excitable or bursting units, whose microscopic dynamics is governed by large sets of coupled stochastic delay-differential equations. This is instigated by the notion that any population displaying a collective ...mode may be treated as macroscopic oscillator. While the framework itself rests on implementing the cumulant approach complemented by the Gaussian approximation, one of the principal gains presents the ability to recast the problem of (stochastic) bifurcations affecting the stability of the stationary state of the exact system in terms of flows containing only several deterministic delaydifferential equations, where noise intensity may act as a bifurcation parameter...

Faculty:
University of Belgrade, Faculty of Physics
Date:
17-12-2013
Projects:
  • Phase Transitions and Characterization of Inorganic and Organic Systems (RS-171015)
Keywords:
excitable dynamics / noise / interaction delays / synchronization / collective mode / cluster states / mean-field model / Gaussian approximation / bifurcation analysis / stochastic bifurcation
[ Google Scholar ]
URI
http://eteze.bg.ac.rs/application/showtheses?thesesId=3659
http://nardus.mpn.gov.rs/handle/123456789/6379
https://fedorabg.bg.ac.rs/fedora/get/o:12463/bdef:Content/download
http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=45078799

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