Effects of delays on neuronal dynamics #

Mustafa Sayli, Stephen Coombes

Poster session

Abstract #

The presence of myelin is a powerful structural factor that controls conduction velocity of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the major source of large-scale brain signals that are seen in EEG/MEG recordings. In this poster, we will aim to combine perspectives from neural mass and network modelling and develop a new set of mathematical tools able to unravel the contributions of space-dependent axonal delays to large-scale spatiotemporal patterning of brain activity. We will first analyse a single neuronal population model with self-feedback (Wilson-Cowan neural mass model) and a fixed delay and show how to construct periodic orbits for a Heaviside firing rate and perform linear stability analysis by augmenting Floquet theory with saltation operations. Then we will consider networks of nonsmooth nodes with a homogeneous delay, and as well as distancedependent heterogeneous delays. Subsequently, we will show how to perform stability and bifurcation analysis of network states (with a particular focus on synchrony). We illustrate how the direct numerical simulations are in excellent agreement with our theory. Finally, we will discuss outstanding challenges for when the delays are plastic.