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.
Author
Franović, Igor T.Mentor
Burić, NikolaCommittee members
Radović, ZoranKnežević, Milan
Elezović-Hadžić, Sunčica
Metadata
Show full item recordAbstract
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...