Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

Visser, Sid and Meijer, Hil G.E. and Putten van, Michel J.A.M and Gils van, Stephan A. (2012) Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays. The Journal of Mathematical Neuroscience, 2 (8). ISSN 2190-8567

Preview

PDF
1475Kb

Abstract:	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.
Item Type:	Article
Copyright:	© 2012 The Author(s)
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Applied Analysis and Mathematical Physics (AAMP) Clinical Neurophysiology (CNPH)
Link to this item:	http://purl.utwente.nl/publications/80800
Official URL:	http://dx.doi.org/10.1186/2190-8567-2-8
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page