Skip to Main Content

Access Provided by Xinjiang University

Physical Review E

Access by Xinjiang University

Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: Theory and experiment

A. Tamaševičius¹, G. Mykolaitis^1,2, V. Pyragas¹, and K. Pyragas^1,3

¹Semiconductor Physics Institute, A. Goštauto 11, LT-01108 Vilnius, Lithuania
²Department of Physics, Vilnius Gediminas Technical University, LT-10223 Vilnius, Lithuania
³Department of Theoretical Physics, Faculty of Physics, Vilnius University, LT-10222 Vilnius, Lithuania

Phys. Rev. E 76, 026203 – Published 6 August, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.026203

Abstract

We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free unstable periodic orbits in nonautonomous chaotic systems. To improve the global control performance we introduce a two-step control algorithm. The problem of a linear stability of the system under delayed feedback control is treated analytically. Theoretical results are confirmed by electronic circuit experiments for a forced double-well oscillator.

Article Text

References (24)

Handbook of Chaos Control, edited by H. G. Schuster (Wiley-VCH, Berlin, 1999).
S. Boccaletti, C. Grebogi, Y. C. Lai, H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
D. J. Gauthier, Am. J. Phys. 71, 750 (2003).
E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
K. Pyragas, Phys. Lett. A 170, 421 (1992).
J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
A. Kittel, J. Parisi, and K. Pyragas, Phys. Lett. A 198, 433 (1995).
Th. Mausbach, Th. Klinger, A. Piel, A. Atipo, Th. Pierre, and G. Bonhomme, Phys. Lett. A 228, 373 (1997).
A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004).
K. Pyragas, Philos. Trans. R. Soc. London, Ser. A 364, 2309 (2006).
W. Just, T. Bernard, M. Ostheimer, E. Reibold, and H. Benner, Phys. Rev. Lett. 78, 203 (1997).
H. Nakajima, Phys. Lett. A 232, 207 (1997).
H. Nakajima and Y. Ueda, Physica D 111, 143 (1998).
B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll, Phys. Rev. Lett. 98, 114101 (2007).
K. Pyragas, Phys. Rev. Lett. 86, 2265 (2001).
K. Pyragas, V. Pyragas, and H. Benner, Phys. Rev. E 70, 056222 (2004); V. Pyragas and K. Pyragas, ibid. 73, 036215 (2006).
K. Höhne, H. Shirahama, C.-U. Choe, H. Benner, K. Pyragas, and W. Just, Phys. Rev. Lett. 98, 214102 (2007).
C. von Loewenich, H. Benner, and W. Just, Phys. Rev. Lett. 93, 174101 (2004).
W. Just, H. Benner, and C. Loewenich, Physica D 199, 33 (2004).
K. Yamasue and T. Hikihara, Phys. Rev. E 69, 056209 (2004).
P. Cvitanović, Phys. Rev. Lett. 61, 2729 (1988).
A. Kittel, K. Pyragas, and R. Richter, Phys. Rev. E 50, 262 (1994).
Y.-Ch. Lai, A. Kandangath, S. Krishnamoorthy, J. A. Gaudet, and A. P. S. de Moura, Phys. Rev. Lett. 94, 214101 (2005).
A. Namajunas, K. Pyragas, and A. Tamaševičius, Phys. Lett. A 201, 42 (1995).