Control by time delayed feedback near a Hopf bifurcation point
| Autor: | Lunel, S. Verduyn, de Wolff, B. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Electron. J. Qual. Theory Differ. Equ. 2017, Paper No. 91, 23 pp |
| Druh dokumentu: | Working Paper |
| DOI: | 10.14232/ejqtde.2017.1.91 |
| Popis: | 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. Comment: 20 pages |
| Databáze: | arXiv |
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