Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays

Koen Dijkstra, Stephanus A. van Gils, S.G. Janssens, Iouri Aleksandrovitsj Kouznetsov, S. Visser

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

Recently, local bifurcation theory for delayed neural fields was developed. In this paper, we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients, respectively. This is done hand in hand with an extensive study of two pitchfork–Hopf bifurcations for a 1D neural field model with ‘Wizard hat’ type connectivity.
Original languageEnglish
Pages (from-to)88-101
Number of pages14
JournalPhysica D
Volume297
DOIs
Publication statusPublished - 15 Mar 2015

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calculus
Bifurcation
Local Bifurcations
evaluation
Bifurcation Theory
symmetry
coefficients
Normal Form
Simplify
Calculus
Connectivity
Symmetry
Evaluation
Coefficient
Model

Keywords

  • EWI-26947
  • IR-100249
  • METIS-316894

Cite this

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title = "Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays",
abstract = "Recently, local bifurcation theory for delayed neural fields was developed. In this paper, we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients, respectively. This is done hand in hand with an extensive study of two pitchfork–Hopf bifurcations for a 1D neural field model with ‘Wizard hat’ type connectivity.",
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Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays. / Dijkstra, Koen ; van Gils, Stephanus A.; Janssens, S.G.; Kouznetsov, Iouri Aleksandrovitsj; Visser, S.

In: Physica D, Vol. 297, 15.03.2015, p. 88-101.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays

AU - Dijkstra, Koen

AU - van Gils, Stephanus A.

AU - Janssens, S.G.

AU - Kouznetsov, Iouri Aleksandrovitsj

AU - Visser, S.

PY - 2015/3/15

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N2 - Recently, local bifurcation theory for delayed neural fields was developed. In this paper, we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients, respectively. This is done hand in hand with an extensive study of two pitchfork–Hopf bifurcations for a 1D neural field model with ‘Wizard hat’ type connectivity.

AB - Recently, local bifurcation theory for delayed neural fields was developed. In this paper, we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients, respectively. This is done hand in hand with an extensive study of two pitchfork–Hopf bifurcations for a 1D neural field model with ‘Wizard hat’ type connectivity.

KW - EWI-26947

KW - IR-100249

KW - METIS-316894

U2 - 10.1016/j.physd.2015.01.004

DO - 10.1016/j.physd.2015.01.004

M3 - Article

VL - 297

SP - 88

EP - 101

JO - Physica D

JF - Physica D

SN - 0167-2789

ER -