Investigating travelling waves in a 2D network of spiking neurons #

Henry Kerr

12:10 Tuesday in 2Q50/51.

Part of the Neurodynamics session.

Abstract #

Spatially extended neuronal networks, as well as their mathematical representations are capable of generating a variety of travelling waves and similar structures, such as self-sustaining localised oscillations, commonly known as bump attractors, and grid-like patterns.

Here, we investigate the existence and stability of travelling waves in a 2D grid of spiking neurons, modelled individually using the leaky integrate-and-fire model augmented with an input variable representing synaptic interactions with the rest of the network. Neurons are connected subject to lateral inhibition: neurons excite each other when close together, but inhibit at medium range.

Among various collective phenomena, this model supports the existence of travelling planar waves, which are mathematically tractable.

We demonstrate the dependence of wave properties upon the form of the connectivity kernel and the timescale of the synaptic buffer. We also examine the linear stability of the wave under spatiotemporal perturbations.