My interests are in mathematical analysis and dynamical systems.
My thesis has centered around: semigroups of linear operators and their adjoints in the context of various classes of delay differential equations, and applications to the analysis of existence, stability, and bifurcation of relatively simple invariants of parameter-dependent nonlinear systems, such as equilibria and periodic orbits. See the publications below.
Pre-prints and publications
S.G. Janssens, A class of abstract delay differential equations in the light of suns and stars. Part II, March 2020, arXiv:2003.13341 [math.DS, math.FA].
Presentation video and slides about this work for the third installment of the Delay Days, online, 1 October 2020.
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]. Accepted for publication in SIAM Journal on Applied Dynamical Systems.
S.G. Janssens, A class of abstract delay differential equations in the light of suns and stars. Part I, January 2019, arXiv:1901.11526 [math.DS, math.FA].
Presentation about this work for a day on Delay equations, theory and applications, Utrecht, 15 February 2019.
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.