TY - JOUR
T1 - Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays
AU - Visser, Sid
AU - Meijer, Hil G.E.
AU - van Putten, Michel J.A.M.
AU - van Gils, Stephan A.
N1 - Open Access
PY - 2012/4/25
Y1 - 2012/4/25
N2 - A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags, is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.
AB - A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags, is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis.
KW - IR-80800
KW - EWI-22021
U2 - 10.1186/2190-8567-2-8
DO - 10.1186/2190-8567-2-8
M3 - Article
VL - 2
JO - Journal of mathematical neuroscience
JF - Journal of mathematical neuroscience
SN - 2190-8567
IS - 8
ER -