Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.51: Poster

Tuesday, February 26, 2008, 16:00–18:00, Poster C

Stabilizing odd-number orbits close to a saddle-node bifurcation by time-delayed feedback control — •Valentin Flunkert¹, Bernold Fiedler¹, Philipp Hövel², Marc Georgi², and Eckehard Schöll¹ — ¹Institut für Theoretische Physik, Technische Universität, Berlin — ²Institut für Mathematik I, Freie Universität, Berlin

We demonstrate by a simple normal form model that an unstable periodic orbit generated by a saddle-node bifurcation can be stabilized using time-delayed feedback control.

This furnishes a further example, besides the subcritical Hopf bifurcation [1], that the alleged ”odd number limitation theorem”, which states that orbits with an odd number of positive Floquet multipliers greater than unity cannot be stabilized by Pyragas time-delayed feedback, does not hold.

We analyse the stability regions of our model in the parameters space and investigate the mechanism of stabilization.

[1] B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll, Phys. Rev. Lett. 98, 114101 (2007).