Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays
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Publication date
2015
Authors
Dijkstra, K.
van Gils, S.A.
Janssens, S.G.
Kuznetsov, Yu.A.
Visser, S.
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Document Type
Article
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taverne
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.
Keywords
neural field, delay equation, normal form, numerical bifurcation analysis, Taverne
Citation
Dijkstra, K, van Gils, S A, Janssens, S G, Kuznetsov, Y A & Visser, S 2015, 'Pitchfork–Hopf bifurcations in 1D neural field models with transmission delays', Physica D: Nonlinear Phenomena, vol. 297, pp. 88-101. https://doi.org/10.1016/j.physd.2015.01.004