Neural Field Models with Transmission Delays and Diffusion
Dynamical Systems
2021-01-29 v3 Functional Analysis
Abstract
A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states, while favouring synchronised oscillatory modes.
Cite
@article{arxiv.1912.09762,
title = {Neural Field Models with Transmission Delays and Diffusion},
author = {Len Spek and Yuri A. Kuznetsov and Stephan A. van Gils},
journal= {arXiv preprint arXiv:1912.09762},
year = {2021}
}