Abstract
Our aim is the stabilization of time-periodic spatio-temporal synchronization patterns. Our primary examples are coupled networks of Stuart-Landau oscillators. We work in the spirit of Pyragas control by noninvasive delayed feedback. In addition we take advantage of symmetry aspects. For simplicity of presentation we first focus on a ring of coupled oscillators. We show how symmetry-breaking controls succeed in selecting and stabilizing unstable periodic orbits of rotating wave type. Standard Pyragas control at minimal period fails in this selection task. Instead, we use arbitrarily small noninvasive time-delays. As a consequence we succeed in stabilizing rotating waves—for arbitrary coupling strengths, and far from equilibrium.
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Acknowledgments
This work originated at, and was supported by the SFB 910 “Control of Self-Organizing Nonlinear Systems: Theoretical Methods and Concepts of Application” of the Deutsche Forschungsgemeinschaft. The authors would like to thank Matthias Bosewitz for fruitful discussions and providing Fig. 6.5. Furthermore, we thank Eckehard Schöll, Ulrike Geiger, Xingjian Zhang, and all the members of the SFB for their many helpful suggestions.
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Schneider, I., Fiedler, B. (2016). Symmetry-Breaking Control of Rotating Waves. In: Schöll, E., Klapp, S., Hövel, P. (eds) Control of Self-Organizing Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-28028-8_6
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DOI: https://doi.org/10.1007/978-3-319-28028-8_6
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