Publications

2010

S.G. Janssens, On a Normalization Technique for Codimension Two Bifurcations of Equilibria of Delay Differential Equations, Master Thesis, Utrecht University, 2010.

Under supervision of Yu.A. Kuznetsov, co-supervised by O. Diekmann.

Two journal articles based in part on this work are in preparation.

The newest versions of the free software package DDE-BIFTOOL contain an implementation for the case of delay differential equations with finitely many constant delays,

\[
\dot{x}(t) = f(x(t), x(t – \tau_1),\ldots,x(t – \tau_m),\alpha)
\]

where $x(t) \in \mathbb{R}^n$, $\alpha \in \mathbb{R}^p$ is a parameter vector and $0 < \tau_1 < \ldots < \tau_m < \infty$. This work was done in collaboration with M.M. Bosschaert, former M.Sc student of Yuri Kuznetsov, now at Hasselt University.

2013

S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, S. Visser, On local bifurcations in neural field models with transmission delays, J. Math. Biol. 66 (2013), no. 4-5, 837–887. (SpringerLinkarXiv)

2015

K. Dijkstra, S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, S. Visser, Pitchfork-Hopf bifurcations in 1D neural field models with transmission delays, Phys. D 297 (2015), 88–101. (ScienceDirect)