Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Responsive and Adaptive Systems (joint session CPP/DY)

DY 2.10: Vortrag

Montag, 1. April 2019, 12:00–12:15, H8

Dissipative systems with nonlocal delayed feedback — •Josua Grawitter, Reinier van Buel, Christian Schaaf, and Holger Stark — Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

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 [Grawitter et al., New J. Phys. 20, 113010 (2018)]. In our model the time it takes a perturbation to travel to the location of measurement is described by an inherent delay time. We investigate the resulting double-delay differential equation using linear stability analysis and numerical integration.

For nonzero delay, linear stability analysis reveals that sufficiently strong feedback destabilizes the system’s trivial fixed point. When feedback is bounded by a smooth sigmoid function, the stability-instability transition follows a supercritical Hopf bifurcation and a stable limit cycle occurs. Its frequency and amplitude respond to parameter changes like the dominant eigenvalue of the linearized problem. In particular, they show similar discontinuities along specific lines. These results are largely independent of the chosen sigmoid function and match previous findings on the feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid. Because our model captures the essential features of nonlocal delayed feedback in dissipative systems, we consider it a valuable reference case for studies of more complex and spatially extended systems such as photoresponsive fluid interfaces.

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