Collective phenomena in networks of spiking neurons with synaptic delays

Abstract

Firing rate models are powerful phenomenological descriptions of the collective activity of large networks of spiking neurons. A prominent feature of the dynamics of large neuronal networks are the synchrony-driven collective oscillations generated by the interplay between synaptic delays and recurrent coupling. This thesis investigates the emergence of delay-induced oscillations in networks of heterogeneous spiking neurons. The analysis is carried out by means of a novel firing rate model that exactly describes the average firing rate and membrane potential dynamics of a network of model spiking neurons (of quadratic integrate-and-fire type). We consider networks with three forms of synaptic delays: i) Fixed delays, ii) Instantaneous rise and single-exponential decay synaptic kinetics, and iii) a combination of the two. For the three forms of synaptic coupling, we obtain phase diagrams analytically to a large extent, which determine the presence of various oscillatory states in regions of the space of parameters of the network. These states include nontrivial synchronous regimes (with quasiperiodic and chaotic dynamics) which are analyzed by performing extensive numerical simulations in the original network of spiking neurons. Finally, comparisons with the traditional firing rate models vastly used in computational neuroscience are performed. In the limit of slow synaptic kinetics and vanishing delays, traditional firing rate models adequately describe the dynamics of the network of spiking neurons. However, for other forms of synaptic delays, the traditional rate equations only provide a faithful description of the network dynamics in the case of strong heterogeneity and inhibitory coupling