o:12463 Collective dynamics and self-organisation of stochastic neuronal systems influenced by synaptic time delay doctoral dissertation Kolektivna dinamika i samoorganizacija stohastičkih neuronskih sistema pod uticajem sinaptičkog kašnjenja : doktorska disertacija en 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... Physics - Condensed matter physics and statistical physics Datum odbrane: 17.12. 2013. excitable dynamics, noise, interaction delays, synchronization,collective mode, cluster states, mean-field model,Gaussian approximation, bifurcation analysis, stochastic bifurcation 538.913(043.3) yes 45078799 91552101 3659 91552100 45078799 2016-08-23T11:01:15.053Z 45 no 46 mentor Igor T. 1979- Franović 2013 63 mentor Nikola, 1959- Burić 2013 63 član komisije Zoran, 1946- Radović 2013 63 član komisije Milan, 1952- Knežević 2013 63 član komisije Sunčica, 1961- Elezović-Hadžić 2013 XIII, 204 lista 7016394 http://phaidrabg.bg.ac.rs/o:12463 no yes 6 2016-08-23T11:01:15.320Z 70 11 1066732 1066764 Physics - Condensed matter physics and statisticalphysics excitable dynamics, noise, interaction delays, synchronization,collective mode, cluster states, mean-field model,Gaussian approximation, bifurcation analysis, stochastic bifurcation 538.913(043.3) 1738 11A16 2013