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

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...

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Bibliographic Details
Published in:Physica. D 2015-03, Vol.297, p.88-101
Main Authors: Dijkstra, K., Gils, S.A. van, Janssens, S.G., Kuznetsov, Yu.A., Visser, S.
Format: Article
Language:English
Subjects:
Delay equation
Neural field
Normal form
Numerical bifurcation analysis
Pitchfork–Hopf bifurcation
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Summary: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. •We study bifurcations in neural field equations with transmission delays.•We focus on symmetry to give an efficient method for spectral computations.•Using residue calculus we show how normal form coefficients can be evaluated.•To illustrate the methods mentioned above we extensively study two particular pitchfork–Hopf bifurcations.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2015.01.004