Conditions for traveling waves in spiking neural networks

Senk, Johanna; Diesmann, Markus; Korvasová, Karolína; Helias, Moritz; Hagen, Espen; Schuecker, Jannis; Tetzlaff, Tom

Preprint

FZJ-2018-01079

Conditions for traveling waves in spiking neural networks

Senk, J. (Corresponding author)FZJ* ; Korvasová, K.FZJ* ; Schuecker, J. ; Hagen, E.FZJ* ; Tetzlaff, T.FZJ* ; Diesmann, M.FZJ* ; Helias, M.FZJ*

2018

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Please use a persistent id in citations: http://hdl.handle.net/2128/17173

Abstract: Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we derive conditions for the existence of spatial and temporal oscillations and periodic traveling waves using linear stability analysis. We first prove that periodic traveling waves cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, traveling waves emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.

Note: 42 pages, 12 figures

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Appears in the scientific report 2018

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OpenAccess