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Neural Field Models with Transmission Delays and Diffusion | | Len Spek
; Yuri A. Kuznetsov
; Stephan A. van Gils
; | | Date: |
20 Dec 2019 | | 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. | | Source: | arXiv, 1912.9762 | | Services: | Forum | Review | PDF | Favorites | |
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