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

Research output: Contribution to journalArticleAcademicpeer-review


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
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - 2015


  • neural field
  • delay equation
  • normal form
  • numerical bifurcation analysis


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