Neural field models with transmission delays and diffusion

Len Spek*, Yu A. Kuznetsov, S.A. van Gils

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models 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.
Original languageEnglish
Article number21
JournalJournal of mathematical neuroscience
Volume10
DOIs
Publication statusPublished - 9 Dec 2020

Keywords

  • UT-Hybrid-D

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