Neural Field Models with Transmission Delays and Diffusion

Len Spek, Yuri A. Kuznetsov, Stephan A. van Gils

Published 2019-12-20Version 1

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.