Stochastic Resonance in Chaotic Spin-Wave Dynamics

We report the first experimental observation of noise-free stochastic resonance by utilizing the intrinsic chaotic dynamics of the system. To this end we have investigated the effect of an external periodic modulation on intermittent signals observed by high power ferromagnetic resonance in yttrium iron garnet spheres. Both the signal-to-noise ratio and the residence time distributions show the characteristic features of stochastic resonance. The phenomena can be explained by means of a one-dimensional intermittent map. We present analytical results as well as computer simulations.Comment: 4 pages, revtex, 5 eps figures included, also available "via www http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html" or "via ftp ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/", Phys. Rev. Lett. in pres

Delayed feedback control of periodic orbits in autonomous systems

For controlling periodic orbits with delayed feedback methods the periodicity has to be known a priori. We propose a simple scheme, how to detect the period of orbits from properties of the control signal, at least if a periodic but nonvanishing signal is observed. We analytically derive a simple expression relating the delay, the control amplitude, and the unknown period. Thus, the latter can be computed from experimentally accessible quantities. Our findings are confirmed by numerical simulations and electronic circuit experimentsComment: 4 pages, Revtex, manuscript also available at ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/prl_98a/ or at http://athene.fkp.physik.th-darmstadt.de/public/wolfram_publ.htm

On the Mechanism of Time--Delayed Feedback Control

The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the success of the control scheme. Our predictions concerning the transient behaviour of the control signal are confirmed by numerical simulations and an electronic circuit experiment.Comment: 4 pages, REVTeX, 4 eps-figures included Phys. Rev. Lett., in press also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.htm

Kontrolle chaotischer Spindynamik mittels zeitverzögerter Rückkopplung

Chaoskontrolle gehört zu den viel versprechendsten Anwendungen der Nichtlinearen Dynamik. Die Methode der zeitverzögerten Rückkopplung hebt sich dabei durch die Einfachheit der experimentellen Umsetzung hervor. Im Rahmen der Zusammenarbeit mit W. Just, TU Darmstadt, sowie J. Holyst, TU Warschau, entstand eine systemunabhängige Theorie, die zum tieferen Verständnis des Kontrollverfahrens beigetragen hat. Dabei wurde stets besonderer Wert auf experimentelle Relevanz gelegt sowie speziell experimentelle Fragestellungen (Verstimmung der Verzögerungszeit, Reglernachlaufzeit) behandelt. Zur Überprüfung der Vorhersagen wurden Experimente an zwei nichtlinearen elektronischen Schwingkreisen durchgeführt. Diese Untersuchungen bilden die Grundlage für die erfolgreiche Anwendung zeitverzögerter Rückkopplungskontrolle in komplexeren Systemen wie der chaotischen Spindynamik in Yttrium-Eisengranat-Kugeln

Theoretical and Experimental aspects of Chaos control by time-delayed feedback

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential systems which are hard to tackle. The essentials ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics