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

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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 languageEnglish
Number of pages30
JournalJournal of mathematical neuroscience
Volume2
Issue number8
DOIs
Publication statusPublished - 25 Apr 2012

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Neocortex
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Keywords

  • IR-80800
  • EWI-22021

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title = "Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays",
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.",
keywords = "IR-80800, EWI-22021",
author = "Sid Visser and Meijer, {Hil G.E.} and {van Putten}, {Michel J.A.M.} and {van Gils}, {Stephan A.}",
note = "Open Access",
year = "2012",
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language = "English",
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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 -