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Collective phenomena in networks of spiking neurons with synaptic delays

Research output: ThesisDoctoral Thesis

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Collective phenomena in networks of spiking neurons with synaptic delays. / Devalle, Federico.

Lancaster University, 2019. 140 p.

Research output: ThesisDoctoral Thesis

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@phdthesis{51bceae0ff734c1199220918f68b946f,
title = "Collective phenomena in networks of spiking neurons with synaptic delays",
abstract = "A prominent feature of the dynamics of large neuronal networks are the synchrony- driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity.",
keywords = "mathematical neuroscience, oscillations, firing rate models, time delays, spiking neurons",
author = "Federico Devalle",
year = "2019",
doi = "10.17635/lancaster/thesis/774",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - THES

T1 - Collective phenomena in networks of spiking neurons with synaptic delays

AU - Devalle, Federico

PY - 2019

Y1 - 2019

N2 - A prominent feature of the dynamics of large neuronal networks are the synchrony- driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity.

AB - A prominent feature of the dynamics of large neuronal networks are the synchrony- driven collective oscillations generated by the interplay between synaptic coupling and synaptic delays. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. Building on recent theoretical advances in exact mean field reductions for neuronal networks, this work explores the dynamics and bifurcations of an exact firing rate model with various forms of synaptic delays. In parallel, the results obtained using the novel firing rate model are compared with extensive numerical simulations of large networks of spiking neurons, which confirm the existence of numerous synchrony-based oscillatory states. Some of these states are novel and display complex forms of partial synchronization and collective chaos. Given the well-known limitation of traditional firing rate models to describe synchrony-based oscillations, previous studies greatly overlooked many of the oscillatory states found here. Therefore, this thesis provides a unique exploration of the oscillatory scenarios found in neuronal networks due to the presence of delays, and may substantially extend the mathematical tools available for modeling the plethora of oscillations detected in electrical recordings of brain activity.

KW - mathematical neuroscience

KW - oscillations

KW - firing rate models

KW - time delays

KW - spiking neurons

U2 - 10.17635/lancaster/thesis/774

DO - 10.17635/lancaster/thesis/774

M3 - Doctoral Thesis

PB - Lancaster University

ER -