Publications

M.M. Bosschaert, S.G. Janssens, Yu.A. Kuznetsov, Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations, March 2019, arXiv:1903.08276 [math.DS].

S.G. Janssens, A class of abstract delay differential equations in the light of suns and stars, January 2019, arXiv:1901.11526 [math.DS, math.FA].

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, DOI: 10.1016/j.physd.2015.01.004.

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, DOI:10.1007/s00285-012-0598-6 and arXiv:1209.2849 [math.DS].

S.G. Janssens, On a Normalization Technique for Codimension Two Bifurcations of Equilibria of Delay Differential Equations, Master Thesis, Utrecht University, 2010, original or with updates (latest: 20 November 2018).

My master thesis was written under supervision of Yu.A. Kuznetsov with Odo Diekmann as co-supervisor. The updated version contains corrections and some new material – see the Summary of updates and corrections. It is available under a Creative Commons BY-NC-ND 4.0 International license.

Software implementations

The code that was originally part of my thesis text is being rewritten and integrated in the DelayTools package for Maple.

Recent versions of the MATLAB and GNU Octave compatible package DDE-BIFTOOL are capable of calculating critical normal form coefficients for local bifurcations, 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 $0 < \tau_1 < \ldots < \tau_m < \infty$. Software implementation in DDE-BIFTOOL is done in cooperation with M.M. Bosschaert (Hasselt, Belgium) and Yu.A. Kuznetsov (Utrecht, The Netherlands).