School of Mathematics

Daniele Avitabile

This is not a bump

This talk discusses patterns in a spatially-extended, deterministic network of synaptically-coupled spiking neurons, which supports coherent structures commonly referred to as “bump” and “wandering bump”, respectively. I will present a new approach to analyse these coherent structures, which lead to the following conclusions:

1. The model does not support a stationary, localised, heterogeneous steady state, therefore the coherent structure is not a bump in the classical sense.

2. In a wide region of parameter space, the model supports countably many coexisting travelling waves. These waves are linearly unstable, have a spatially localised profile, and a vanishingly small speed.

I will show numerical evidence that the structures known as “bump” and “wandering bump” are a special type of spatio-temporal chaos, and their existence is underpinned by the bifurcation structure of the travelling waves mentioned above.