Berlin 2018 – scientific programme

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BP: Fachverband Biologische Physik

BP 34: Neuroscience

BP 34.8: Talk

Thursday, March 15, 2018, 17:00–17:15, H 1058

Control of Wave Propagation in Neural Field Equations — Alexander Ziepke, •Steffen Martens, and Harald Engel — Technische Universität Berlin, Institut für Theoretische Physik, 10623 Berlin, Germany

The investigation of neural fields, describing dynamics of large networks of synaptically coupled neurons by means of continuous field equations, has gained interest over the last decades. In particular, neural field systems exhibit self-organized spatio-temporal structures, such as stationary and traveling fronts and pulses, spiral waves, and localized spot-like bump solutions. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception and visual hallucinations, to name a few. Due to the important applications of neural field models, the question arises how to effectively control solutions in these systems.

In order to address this problem, we extend analytic control techniques, previously derived for reaction-diffusion systems [J. Löber, PRL 112, 148305; arXiv:1703.04246], to neural field equations. The proposed open-loop control scheme enables shifting and rotating traveling bump and wave solutions according to a prescribed protocol of motion while simultaneously conserving their shape. Noteworthy, the control signal solely depends on the profile and velocity of the unperturbed solution, and thus, for applying the control scheme, a detailed knowledge of the internal dynamics is not required.