Nonlinear Dynamics at the Free University Berlin

Winter 2021-2022

Oberseminar Nonlinear Dynamics



Tuesday, 2.11.2021 Prof. Jaroslav Hlinka (Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic) Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators
The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this work, we analyze white and how perturbations, exogenous or endogenous, may promote or delay seizure emergence [1], following previous observations in vivo, in vitro and in silico [2]. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures. References

Time and Place

Because of the current Corona virus situation, the events take place online.

Guests are always welcome !


switch Last change: Oct. 25, 2021
This page strictly conforms to the XHTMLswitch1.0 standard and uses style sheets. Valid XHTML 1.0! Valid CSS!