Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays
1 Department of Applied Mathematics, University of Twente, Enschede, 7500, The Netherlands
2 MIRA Institute for Biomedical Engineering and Technical Medicine, University of Twente, Enschede, 7500, The Netherlands
3 Department of Clinical Neurophysiology, Medisch Spectrum Twente, Enschede, 7500, The Netherlands
The Journal of Mathematical Neuroscience 2012, 2:8 doi:10.1186/2190-8567-2-8Published: 25 April 2012
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.