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

Sid Visser; Hil G.E. Meijer; Michel J.A.M. van Putten; Stephan A. van Gils

doi:10.1186/2190-8567-2-8

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

Sid Visser, Hil G.E. Meijer, Michel J.A.M. van Putten, Stephan A. van Gils

Faculty of Science and Technology

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

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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.

Original language	English
Number of pages	30
Journal	Journal of mathematical neuroscience
Volume	2
Issue number	8
DOIs	https://doi.org/10.1186/2190-8567-2-8
Publication status	Published - 25 Apr 2012

Keywords

IR-80800
EWI-22021

Access to Document

10.1186/2190-8567-2-8Licence: CC BY

Visser2012analysis
open
Final published version, 1.44 MBLicence: CC BY

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Visser, S., Meijer, H. G. E., van Putten, M. J. A. M., & van Gils, S. A. (2012). Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays. Journal of mathematical neuroscience, 2(8). https://doi.org/10.1186/2190-8567-2-8

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