Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Posters II

DY 30.30: Poster

Donnerstag, 25. März 2010, 16:00–18:00, Poster C

Floquet Stability Analysis of Memory Difference Control — •David Conal Higgins and Jens Christian Claussen — Institut für Neuro- und Bioinformatik, Universität zu Lübeck

A time discrete version of Pyragas control [1], difference control, was introduced by Bielawski, Derozier and Glorieux [2] and acts in the Poincaré section. It allows stabilization of orbits with Ljapunov number between -3 and -1. Outside of this range, the scheme can be extended by an additional term (MDC, memory difference control) as introduced in [3]. In general, Poincaré-based control schemes may show limitations in the length of the control impulse, which is relevant in the case of difference control [4]. The stability can be analyzed by Floquet theory, giving rise to a special class of delay differential equations. Here we analyze the stability properties of MDC by means of a Floquet stability analysis.

[1] K. Pyragas, Phys. Lett. A 170, 421 (1992)

[2] S. Bielawski, D. Derozier and P. Glorieux, Phys. Rev. A 42, 2492 (1993)

[3] J. C. Claussen, T. Mausbach, A. Piel, H. G. Schuster, Phys. Rev. E 58, 7256 (1998)

[4] J. C. Claussen, New J. Phys. 10, 063003 (2008)