Stroboscopic control and tracking of periodic states

Springer Science and Business Media LLC - Tập 112 - Trang 1261-1274 - 2023
Anna Dittus1, Niklas Kruse1, Hannes Wallner1,2, Lukas Böttcher2, Ingo Barke2, Sylvia Speller2, Jens Starke1, Wolfram Just1
1Institute of Mathematics, University of Rostock, Rostock, Germany
2Institute of Physics, University of Rostock, Rostock, Germany

Tóm tắt

Numerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately, the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states which can be ultimately implemented in real-world experimental set-ups. Taking inspiration from atomic force microscopy, we develop experimentally relevant control and tracking tools for time periodic solutions in driven nonlinear oscillator systems based on stroboscopic maps.

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