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Eliminating restrictions of time-delayed feedback control using equivariance
1. | Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany, Germany |
References:
[1] |
M. Bosewitz, Stabilisierung gekoppelter Oszillatoren durch verzögerte Rückkopplungs-kontrolle, (German) [Stabilization of coupled oscillators by delayed feedback-control] Bachelor Thesis, Freie Universität Berlin, 2013. |
[2] |
K. Bubolz, Stabilisierung periodischer Orbits im System zweier gekoppelter Oszillatoren durch zeitverzögerte Rückkopplungskontrolle, (German) [Stabilization of periodic orbits in a system of two coupled oscillators by time-delayed feedback-control] Bachelor Thesis, Freie Universität Berlin, 2013. |
[3] |
B. Fiedler, Global Bifurcation of Periodic Solutions with Symmetry, Lect. Notes Math. 1309, Springer-Verlag, Heidelberg, 1988. |
[4] |
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel and E. Schöll, Refuting the odd number limitation of time-delayed feedback control, Phys. Rev. Lett., 98 (2007), 114101.
doi: 10.1103/PhysRevLett.98.114101. |
[5] |
B. Fiedler, V. Flunkert, P. Hövel and E. Schöll, Delay stabilization of periodic orbits in coupled oscillator systems, Phil. Trans. R. Soc. A, 368 (2010), 319-341.
doi: 10.1098/rsta.2009.0232. |
[6] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, Delay Equations: Functional-, Complex-, and Nonlinear Analysis, Applied Mathematical Sciences Vol. 110, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
[7] |
M. Golubitsky, I. Stewart and D. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. 2. AMS 69, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-4574-2. |
[8] |
M. Golubitsky and I. Stewart, The Symmetry Perspective. From Equilibrium to Chaos in Phase Space and Physical Space, Progress in Mathematics, Volume 200, Birkhäuser, Basel, 2002.
doi: 10.1007/978-3-0348-8167-8. |
[9] |
C. M. Postlethwaite, G. Brown and M. Silber, Feedback control of unstable periodic orbits in equivariant Hopf bifurcation problems, Phil. Trans. R. Soc. A, 371 (2013), 20120467, 20pp.
doi: 10.1098/rsta.2012.0467. |
[10] |
K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170 (1992), 421-428. |
[11] |
K. Pyragas, A twenty-year review of time-delay feedback control and recent developments, in International Symposium on Nonlinear Theory and its Applications, 1 (2012), 683-686.
doi: 10.15248/proc.1.683. |
[12] |
I. Schneider, Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf bifurcation, Phil. Trans. R. Soc. A, 371 (2013), 20120472, 10pp.
doi: 10.1098/rsta.2012.0472. |
[13] |
I. Schneider, Equivariant Pyragas Control, Master Thesis, Freie Universität Berlin, 2014. |
show all references
References:
[1] |
M. Bosewitz, Stabilisierung gekoppelter Oszillatoren durch verzögerte Rückkopplungs-kontrolle, (German) [Stabilization of coupled oscillators by delayed feedback-control] Bachelor Thesis, Freie Universität Berlin, 2013. |
[2] |
K. Bubolz, Stabilisierung periodischer Orbits im System zweier gekoppelter Oszillatoren durch zeitverzögerte Rückkopplungskontrolle, (German) [Stabilization of periodic orbits in a system of two coupled oscillators by time-delayed feedback-control] Bachelor Thesis, Freie Universität Berlin, 2013. |
[3] |
B. Fiedler, Global Bifurcation of Periodic Solutions with Symmetry, Lect. Notes Math. 1309, Springer-Verlag, Heidelberg, 1988. |
[4] |
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel and E. Schöll, Refuting the odd number limitation of time-delayed feedback control, Phys. Rev. Lett., 98 (2007), 114101.
doi: 10.1103/PhysRevLett.98.114101. |
[5] |
B. Fiedler, V. Flunkert, P. Hövel and E. Schöll, Delay stabilization of periodic orbits in coupled oscillator systems, Phil. Trans. R. Soc. A, 368 (2010), 319-341.
doi: 10.1098/rsta.2009.0232. |
[6] |
O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel and H. O. Walther, Delay Equations: Functional-, Complex-, and Nonlinear Analysis, Applied Mathematical Sciences Vol. 110, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4206-2. |
[7] |
M. Golubitsky, I. Stewart and D. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. 2. AMS 69, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-4574-2. |
[8] |
M. Golubitsky and I. Stewart, The Symmetry Perspective. From Equilibrium to Chaos in Phase Space and Physical Space, Progress in Mathematics, Volume 200, Birkhäuser, Basel, 2002.
doi: 10.1007/978-3-0348-8167-8. |
[9] |
C. M. Postlethwaite, G. Brown and M. Silber, Feedback control of unstable periodic orbits in equivariant Hopf bifurcation problems, Phil. Trans. R. Soc. A, 371 (2013), 20120467, 20pp.
doi: 10.1098/rsta.2012.0467. |
[10] |
K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170 (1992), 421-428. |
[11] |
K. Pyragas, A twenty-year review of time-delay feedback control and recent developments, in International Symposium on Nonlinear Theory and its Applications, 1 (2012), 683-686.
doi: 10.15248/proc.1.683. |
[12] |
I. Schneider, Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf bifurcation, Phil. Trans. R. Soc. A, 371 (2013), 20120472, 10pp.
doi: 10.1098/rsta.2012.0472. |
[13] |
I. Schneider, Equivariant Pyragas Control, Master Thesis, Freie Universität Berlin, 2014. |
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