Control by time delayed feedback near a Hopf bifurcation point
In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2017-12-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6042 |
| _version_ | 1797830554546077696 |
|---|---|
| author | Sjoerd Verduyn Lunel Babette de Wolff |
| author_facet | Sjoerd Verduyn Lunel Babette de Wolff |
| author_sort | Sjoerd Verduyn Lunel |
| collection | DOAJ |
| description | In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying the Floquet multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation. |
| first_indexed | 2024-04-09T13:37:56Z |
| format | Article |
| id | doaj.art-0924c40108964592b7baffd2e7d61563 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:56Z |
| publishDate | 2017-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-0924c40108964592b7baffd2e7d615632023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-12-0120179112310.14232/ejqtde.2017.1.916042Control by time delayed feedback near a Hopf bifurcation pointSjoerd Verduyn Lunel0Babette de Wolff1Mathematical Institute, Utrecht University, Utrecht, The NetherlandsMathematical Institute, Utrecht University, Utrecht, The NetherlandsIn this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1) by directly studying the Floquet multipliers and 2) by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6042pyragas controltime delayed feedback controlhopf bifurcationneutral equations |
| spellingShingle | Sjoerd Verduyn Lunel Babette de Wolff Control by time delayed feedback near a Hopf bifurcation point Electronic Journal of Qualitative Theory of Differential Equations pyragas control time delayed feedback control hopf bifurcation neutral equations |
| title | Control by time delayed feedback near a Hopf bifurcation point |
| title_full | Control by time delayed feedback near a Hopf bifurcation point |
| title_fullStr | Control by time delayed feedback near a Hopf bifurcation point |
| title_full_unstemmed | Control by time delayed feedback near a Hopf bifurcation point |
| title_short | Control by time delayed feedback near a Hopf bifurcation point |
| title_sort | control by time delayed feedback near a hopf bifurcation point |
| topic | pyragas control time delayed feedback control hopf bifurcation neutral equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6042 |
| work_keys_str_mv | AT sjoerdverduynlunel controlbytimedelayedfeedbacknearahopfbifurcationpoint AT babettedewolff controlbytimedelayedfeedbacknearahopfbifurcationpoint |