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Main Title: Dissipative systems with nonlocal delayed feedback control
Author(s): Grawitter, Josua
van Buel, Reinier
Schaaf, Christian
Stark, Holger
Type: Article
Language Code: en
Abstract: We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a nonzero system delay acts to destabilize the otherwise stable fixed point for sufficiently large feedback strengths. The imaginary part of the dominant eigenvalue is bounded by twice the feedback strength. In the relevant parameter space it changes discontinuously along specific lines when switching between eigenvalues. When the feedback control force is bounded by a sigmoid function, a supercritical Hopf bifurcation occurs at the stability–instability transition. Perturbing the fixed point, the frequency and amplitude of the resulting limit cycles respond to parameter changes like the dominant eigenvalue. In particular, they show similar discontinuities along specific lines. These results are largely independent of the exact shape of the sigmoid function. Our findings match well with previously reported results on a feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid (Zeitz et al 2015 Eur. Phys. J. E 38 22). Thus, our model captures the essential features of nonlocal delayed feedback control in spatially extended dissipative systems.
Issue Date: 7-Nov-2018
Date Available: 26-Nov-2018
DDC Class: 530 Physik
Subject(s): time-delayed feedback
closed-loop control
soft matter
nonlocal control
spatiotemporal dynamics
double delay
Sponsor/Funder: DFG, TH 662/19-1, Open Access Publizieren 2017 - 2018 / Technische Universität Berlin
Journal Title: New Journal of Physics
Publisher: IOP Publishing
Publisher Place: London
Volume: 20
Issue: 11
Article Number: 113010
Publisher DOI: 10.1088/1367-2630/aae998
EISSN: 1367-2630
Appears in Collections:FG Statistische Physik weicher Materie und biologischer Systeme » Publications

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