TY - JOUR
T1 - Neural field models with transmission delays and diffusion
AU - Spek, Len
AU - Kuznetsov, Yu.A.
AU - van Gils, S.A.
N1 - Springer deal
PY - 2020/12/9
Y1 - 2020/12/9
N2 - 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.
AB - 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.
U2 - 10.1186/s13408-020-00098-5
DO - 10.1186/s13408-020-00098-5
M3 - Article
SN - 2190-8567
VL - 10
JO - Journal of mathematical neuroscience
JF - Journal of mathematical neuroscience
M1 - 21
ER -