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Entropy 2018, 20(7), 502; https://doi.org/10.3390/e20070502

Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles

Northumbria University, Newcastle upon Tyne NE1 8ST, UK
Received: 31 May 2018 / Revised: 27 June 2018 / Accepted: 28 June 2018 / Published: 1 July 2018
(This article belongs to the Special Issue Coherence in Open Quantum Systems)
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Abstract

Sets in the parameter space corresponding to complex exceptional points (EP) have high codimension, and by this reason, they are difficult objects for numerical location. However, complex EPs play an important role in the problems of the stability of dissipative systems, where they are frequently considered as precursors to instability. We propose to locate the set of complex EPs using the fact that the global minimum of the spectral abscissa of a polynomial is attained at the EP of the highest possible order. Applying this approach to the problem of self-stabilization of a bicycle, we find explicitly the EP sets that suggest scaling laws for the design of robust bikes that agree with the design of the known experimental machines. View Full-Text
Keywords: exceptional points in classical systems; coupled systems; non-holonomic constraints; nonconservative forces; stability optimization; spectral abscissa; swallowtail; bicycle self-stability exceptional points in classical systems; coupled systems; non-holonomic constraints; nonconservative forces; stability optimization; spectral abscissa; swallowtail; bicycle self-stability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kirillov, O.N. Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles. Entropy 2018, 20, 502.

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