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

K. Dijkstra; S.A. van Gils; S.G. Janssens; Yu.A. Kuznetsov; S. Visser

doi:10.1016/j.physd.2015.01.004

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

K. Dijkstra^*, S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, S. Visser

^*Corresponding author for this work

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

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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 language	English
Pages (from-to)	88-101
Number of pages	14
Journal	Physica D
Volume	297
Early online date	28 Jan 2015
DOIs	https://doi.org/10.1016/j.physd.2015.01.004
Publication status	Published - 15 Mar 2015

Keywords

Neural field
Delay equation
Normal form
Numerical bifurcation analysis
Pitchfork-Hopf bifurcation
2023 OA procedure

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10.1016/j.physd.2015.01.004

ArticleFinal published version, 2.41 MBLicence: Taverne

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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 {\textquoteleft}Wizard hat{\textquoteright} type connectivity.",

keywords = "Neural field, Delay equation, Normal form, Numerical bifurcation analysis, Pitchfork-Hopf bifurcation, 2023 OA procedure",

author = "K. Dijkstra and {van Gils}, S.A. and S.G. Janssens and Yu.A. Kuznetsov and S. Visser",

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AU - Dijkstra, K.

AU - van Gils, S.A.

AU - Janssens, S.G.

AU - Kuznetsov, Yu.A.

AU - Visser, S.

PY - 2015/3/15

Y1 - 2015/3/15

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 - Neural field

KW - Delay equation

KW - Normal form

KW - Numerical bifurcation analysis

KW - Pitchfork-Hopf bifurcation

KW - 2023 OA procedure

U2 - 10.1016/j.physd.2015.01.004

DO - 10.1016/j.physd.2015.01.004

M3 - Article

SN - 0167-2789

VL - 297

SP - 88

EP - 101

JO - Physica D

JF - Physica D

ER -

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

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Keywords

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