Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles
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 co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/7/502 |
| _version_ | 1798004879792275456 |
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| author | Oleg N. Kirillov |
| author_facet | Oleg N. Kirillov |
| author_sort | Oleg N. Kirillov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T12:31:37Z |
| format | Article |
| id | doaj.art-bc4ff6ad970e4572aa01716a11aa8808 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:31:37Z |
| publishDate | 2018-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bc4ff6ad970e4572aa01716a11aa88082022-12-22T04:23:45ZengMDPI AGEntropy1099-43002018-07-0120750210.3390/e20070502e20070502Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of BicyclesOleg N. Kirillov0Northumbria University, Newcastle upon Tyne NE1 8ST, UKSets 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.http://www.mdpi.com/1099-4300/20/7/502exceptional points in classical systemscoupled systemsnon-holonomic constraintsnonconservative forcesstability optimizationspectral abscissaswallowtailbicycle self-stability |
| spellingShingle | Oleg N. Kirillov Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles Entropy exceptional points in classical systems coupled systems non-holonomic constraints nonconservative forces stability optimization spectral abscissa swallowtail bicycle self-stability |
| title | Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles |
| title_full | Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles |
| title_fullStr | Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles |
| title_full_unstemmed | Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles |
| title_short | Locating the Sets of Exceptional Points in Dissipative Systems and the Self-Stability of Bicycles |
| title_sort | locating the sets of exceptional points in dissipative systems and the self stability of bicycles |
| topic | exceptional points in classical systems coupled systems non-holonomic constraints nonconservative forces stability optimization spectral abscissa swallowtail bicycle self-stability |
| url | http://www.mdpi.com/1099-4300/20/7/502 |
| work_keys_str_mv | AT olegnkirillov locatingthesetsofexceptionalpointsindissipativesystemsandtheselfstabilityofbicycles |