ELFT HÍRADÓ

[Szeminárium koordinátor <sem-admin AT szfki.hu>]

SZFI SeminarPolner MónikaSZTE, Bolyai Intézet (host: Varró Sándor) 
Bifurcations of neural fields on the sphereTuesday, 20 September 2022, 10:00, 
KFKI Campus, Bldg. 1, 2nd floor, Conference RoomA natural model to study 
pattern formation in large groups of neurons is the neural field. We 
investigate a neural field model on a sphere, with excitatory and inhibitory 
neurons, with space-dependent delays and gap junctions. This work is an 
extension of [1] in the following directions: we add a diffusion term to the 
model to simulate gap junctions. Moreover, we consider two distinct 
populations of excitatory and inhibitory neurons in a Wilson-Cowan type 
model, instead of an Amari type model. The main focus is on the investigation 
of pattern formation in these systems on the sphere. Specifically, we look in 
detail at the periodic and quasi periodic orbits which are generated by Hopf 
bifurcation in the presence of spherical symmetry. We derive formulas to 
compute the normal form coefficients of these bifurcations and predict the 
stability of the resulting branches. All these results are used to study the 
effect of the gap junctions on the resulting patterns of the neural field. 
Predictions of the emerging spatio-temporal patterns are found to be in 
excellent agreement with the results from our direct numerical simulations. 
The numerical method which we develop is an extension of the method used in 
[1] for solving integro-differential equations with delays on large meshes. 
We show the advantage of using cubic Hermite splines for interpolating the 
history of delay differential equation. On an almost regular triangulation of 
the two-sphere, derived from the icosahedron, we discretize the surface 
Laplacian using finite difference formulas. Finally, for time integration we 
employ an implicit-explicit scheme, where the linear diffusion term is 
evaluated implicitly and the nonlinear synaptic term is evaluated explicitly. 
[1] S. Visser, R. Nicks, O. Faugeras, and S. Coombes, Standing and travelling 
waves in a spherical brain model: The Nunez model revisited, Physica D, 349 
(2017), pp. 27-45 Minden érdeklődőt szívesen látunk! - Everyone is 
welcome to attend.Attila Nagysem-admin AT szfki.hu