prof.dr. S.A. van Gils (Stephan)

Chair holder for Nonlinear Analysis

About Me

Stephan van Gils holds the chair for Nonlinear Analysis in the department of Applied Mathematics at the University of Twente.

Short CV

born on 1 November 1954
1973-1979: Mathematics at the Free University Amsterdam
1979-1984: PhD in Mathematics at the CWI in Amsterdam (advisor Odo Diekmann)
1985-1987: Postdoc at the Free University Amsterdam with Jan Sanders
1985         : Fulbright Fellowship, Postdoc at Michigan State University with Shui-Nee Chow
1986         : Postdoc at the University of Houston with Marty Golubitsky 
1987-2000: Assistant Professor at Dept. of Applied Mathematics, University of Twente
2000-2004: Associate Professor at Dept. of Applied Mathematics, University of Twente
2004-2009: Programme Director Applied Mathematics
2004-........: Professor of Nonlinear Analysis, University of Twente
2009-........: Chair Applied Analysis, University of Twente
2016-2018: Head of Department Applied Mathematics


Parkinson Disease
Basal Ganglia
Deep Brain Stimulation
Sine-Gordon Equation
Vortex Flow
Subthalamic Nucleus
Bias Currents


Delay differential equations

Delay differential equations are characterized by the fact that the rate of change of the present state depends on the history of the state. There are many examples, notably in the field of biology, but also in physical systems and economy. Over the past 30 years the general theory for this class of equations has been shaped much in the spirit of the qualitative theory for ordinary differential equations.

When the state space is the n-dimensional Euclidian space, a complete description of the dynamics in the neighborhood of an equilibrium is well known, including the normal form equation on the center manifold.

The goal is to extend this to cases where the state space is infinite dimensional and the linear part of the equation contains an unbounded operator like diffusion.

Mathematical neuroscience

Neural field equations where introduced by Amari, Wilson and Cowan in the seventies of the previous century. It is a continuum description of electrical activity in the brain based on averaging over both space and time. In terms of mathematics it is an integro-differential equation and due to the transmission delays and synaptic handling it is an example of an abstract delay differential equation.

The goal is to link this equation to human data. This is an extremely challenging inverse problem where we try to identify the local and nonlocal connectivity and the (nonlinear) sigmoidal gain function from recordings of the brain.


It is a challenging problem to identify the part of cortex that must be resected, the epileptic zone, in order to stop focal epileptic seizures. Our goal is to build a network of dynamic nodes, based on human cortical SPES (Single Pulse Electric Stimulation) and to determine from the dynamics of the network the epileptic zone. This research is done in collaboration with the University Medical Center Utrecht (UMCU). 

Parkinson’s disease

Parkinson’s disease a neurodegenerative disorder. When medication does not relieve the symptoms, deep brain stimulation (DBS) is one of the options where the subthalamic nucleus is stimulated continuously at 130 HZ. In the first decade of the century Peter Tass promoted another way of simulation, the so called coordinated reset (CR) stimulation.

In cooperation with the medical centers of Nijmegen and Maastricht, we investigate the plasticity rules that govern the dynamics of the basal ganglia, make simulation models for the basal ganglia that incorporate these rules, and perform a CR-trial on Parkinson patients.


Recent Articles
Eissa, T. L., Dijkstra, K., Brune, C., Emerson, R. G., Van Putten, M. J. A. M., Goodman, R. R., ... van Gils, S. A. (2017). Cross-scale effects of neural interactions during human neocortical seizure activity. Proceedings of the National Academy of Sciences of the United States of America, 114(40), 10761-10766. DOI: 10.1073/pnas.1702490114
Meijer, H. G. E., Eissa, T. L., Kiewiet, B., Neuman, J. F., Schevon, C. A., Emerson, R. G., ... van Drongelen, W. (2015). Modeling Focal Epileptic Activity in the Wilson-Cowan Model with Depolarization Block. Journal of mathematical neuroscience, 5(1), 7. DOI: 10.1186/s13408-015-0019-4

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Visiting Address

University of Twente
Faculty of Electrical Engineering, Mathematics & Computer Science
Zilverling (building no. 11), room 3042
Hallenweg 19
7522NH  Enschede
The Netherlands

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University of Twente
Faculty of Electrical Engineering, Mathematics & Computer Science
Zilverling  3042
P.O. Box 217
7500 AE Enschede
The Netherlands

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