Robust Stability at the Swallowtail Singularity
Consider the set of monic fourth-order real polynomials transformedso that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2013-12-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00024/full |
| _version_ | 1811306687264456704 |
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| author | Oleg N. Kirillov Michael eOverton |
| author_facet | Oleg N. Kirillov Michael eOverton |
| author_sort | Oleg N. Kirillov |
| collection | DOAJ |
| description | Consider the set of monic fourth-order real polynomials transformedso that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four. Motivated by this example, we review recent works on robust stability, abscissa optimization, heavily damped systems, dissipation-induced instabilities, and eigenvalue dynamics in order to point out some connections that appear to be not widely known. |
| first_indexed | 2024-04-13T08:49:56Z |
| format | Article |
| id | doaj.art-8143d5316e884625ba6cc613767385b8 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-13T08:49:56Z |
| publishDate | 2013-12-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-8143d5316e884625ba6cc613767385b82022-12-22T02:53:30ZengFrontiers Media S.A.Frontiers in Physics2296-424X2013-12-01110.3389/fphy.2013.0002471486Robust Stability at the Swallowtail SingularityOleg N. Kirillov0Michael eOverton1Helmholtz-Zentrum Dresden-RossendorfNew York UniversityConsider the set of monic fourth-order real polynomials transformedso that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four. Motivated by this example, we review recent works on robust stability, abscissa optimization, heavily damped systems, dissipation-induced instabilities, and eigenvalue dynamics in order to point out some connections that appear to be not widely known.http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00024/fulloptimizationWhitney umbrellaAbscissaoverdampingasymptotic stabilitySwallowtail |
| spellingShingle | Oleg N. Kirillov Michael eOverton Robust Stability at the Swallowtail Singularity Frontiers in Physics optimization Whitney umbrella Abscissa overdamping asymptotic stability Swallowtail |
| title | Robust Stability at the Swallowtail Singularity |
| title_full | Robust Stability at the Swallowtail Singularity |
| title_fullStr | Robust Stability at the Swallowtail Singularity |
| title_full_unstemmed | Robust Stability at the Swallowtail Singularity |
| title_short | Robust Stability at the Swallowtail Singularity |
| title_sort | robust stability at the swallowtail singularity |
| topic | optimization Whitney umbrella Abscissa overdamping asymptotic stability Swallowtail |
| url | http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00024/full |
| work_keys_str_mv | AT olegnkirillov robuststabilityattheswallowtailsingularity AT michaeleoverton robuststabilityattheswallowtailsingularity |