3 research outputs found
Conditions for wave trains in spiking neural networks
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 employ liner stability analysis
to derive conditions for the existence of spatial and temporal oscillations and
wave trains, that is, temporally and spatially periodic traveling waves. We
first prove that wave trains 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, wave
trains 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.Comment: 36 pages, 8 figures, 4 table
Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations
International audienceNeural field equations describe the activity of neural populations at a mesoscopic level. Although the early derivation of these equations introduced space dependent delays coming from the finite speed of signal propagation along axons, there have been few studies concerning their role in shaping the (nonlinear) dynamics of neural activity. This is mainly due to the lack of analytical tractable models. On the other hand, constant delays have been introduced to model the synaptic transmission and the spike initiation dynamics. By incorporating the two kinds of delays into the neural field equations, we are able to find the Hopf bifurcation curves analytically, which produces many Hopf--Hopf interactions. We use normal theory to study two different types of connectivity that reveal a surprisingly rich dynamical portrait. In particular, the shape of the connectivity strongly influences the spatiotemporal dynamics