Chaos
Feedback | Help | Exit
Chaos
   
 
 
 
Previous Article
The OPCL control method for entrainment, model-resonance, and migration actions on multiple-attractor systems
A survey is given of three different control objectives that can be achieved with the use of the Open-Plus-Closed-Loop (OPCL) control method, developed by Jackson and Grosu. For a system that can be c...
Next Article
Sharp diffraction peaks from chaotic structures
Recently various models for spatially chaotic structures have been proposed. We study the diffraction patterns produced by plane chaotic waves incident on one-dimensional chaotic point scatterers. The...

Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis

Chaos 7, 560 (1997); doi:10.1063/1.166256

Issue Date: December 1997

You are not logged in to this journal. Log in

David W. Sukow, Michael E. Bleich, Daniel J. Gauthier, and Joshua E. S. Socolar
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, P.O. Box 90305, Durham, North Carolina 27708
We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control. ©1997 American Institute of Physics.
History: Received 24 March 1997; accepted 21 May 1997
Permalink: http://link.aip.org/link/?CHAOEH/7/560/1
BUY THIS ARTICLE   (US$28)
Download PDF (368 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 05.45.+b
    Statistical physics and thermodynamics Theory and models of chaotic systems
  • 84.30.Bv
    Electronics: radiowave and microwave technology; direct energy conversion and storage Electronic circuits Circuit theory (including computer-aided circuit design and analysis)
  • 84.30.Yq
    Electronics: radiowave and microwave technology; direct energy conversion and storage Electronic circuits Other electronic circuits
  • YEAR: 1996-97

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (57)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992).
  2. E. Ott and M. Spano, Phys. Today 48, 34 (1995).
  3. In the nomenclature of modern control engineering, a control protocol that stabilizes a system about a state that is inherently part of the system is called a regulator control scheme.
  4. A system ergodically explores the neighborhoods of the infinite number of unstable states when it is chaotic. Targeting techniques can be used to direct the system to the desired state.
  5. K. Petermann, IEEE J. Sel. Top. Quantum Electron. 1, 480 (1995), and references therein.
  6. G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995), and references therein.
  7. Y. Liu, N. Kikuchi, and J. Ohtsubo, Phys. Rev. E 51, 2697 (1995), and references therein.
  8. J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
  9. K. Pyragas, Phys. Lett. A 170, 421 (1992).
  10. M. E. Bleich and J. E. S. Socolar, Phys. Lett. A 210, 87 (1996).
  11. M. Ciofini, R. Meucci, and F. T. Arecchi, Phys. Rev. E 52, 94 (1995), and references therein.
  12. R. Mettin and T. Kurz, Phys. Lett. A 206, 331 (1995), and references therein.
  13. R. Mettin, A. Hübler, and A. Scheeline, Phys. Rev. E 51, 4065 (1995).
  14. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1190).
  15. Typically, Modern Control Engineers use a different, but equivalent, method for expressing the perturbations. For example, it is common to find the perturbations expressed as deltapi = pi−p-bar = −KT[zi−z*(p-bar)] where KT is a 1×m feedback matrix ( Ref. 16).
  16. K. Ogatga, Modern Control Engineering, 2nd Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1990).
  17. W. L. Ditto, S. N. Rauseo, and M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
  18. E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
  19. B. Peng, V. Petrov, and K. Showalter, J. Phys. C 95, 4957 (1991).
  20. T. W. Carr and I. B. Schwartz, Phys. Rev. E 50, 3410 (1995).
  21. T. W. Carr and I. B. Schwartz, Phys. Rev. E 51, 5109 (1995).
  22. Z. Qu, G. Hu, and B. Ma, Phys. Lett. A 178, 265 (1993).
  23. S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993).
  24. G. A. Johnson and E. R. Hunt, IEEE Trans. Circuits Syst. 40, 833 (1993).
  25. K. Pyragas and T. Tama[s-caron]evi[c-caron]ius, Phys. Lett. A 180, 99 (1993).
  26. D. J. Gauthier, D. W. Sukow, H. M. Concannon, and J. E. S. Socolar, Phys. Rev. E 50, 2343 (1994).
  27. A. Namaj[u-bar]nas, K Pyragas, A. Tama[s-caron]evi[c-caron]ius, Phys. Lett. A 204, 255 (1995).
  28. S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. E 49, R971 (1994).
  29. Th. Pierre, G. Bonhomme and A. Atipo, Phys. Rev. Lett. 76, 2290 (1996).
  30. T. Hikihara and T. Kawagoshi, Phys. Lett. A 211, 29 (1996).
  31. M. Ye, D. W. Peterman, and P. E. Wigen, Phys. Lett. A 203, 23 (1995).
  32. E. Schöll and K. Pyragas, Europhys. Lett. 24, 159 (1993).
  33. C. Lourenço and A. Babloyantz, Neural Comput. 6, 1141 (1994).
  34. W. Lu and R. G. Harrison, Opt. Commun. 109, 457 (1994).
  35. C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
  36. R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996).
  37. K. Pyragas, Phys. Lett. A 206, 323 (1995).
  38. A map-based version of ETDAS was proposed independently by E. H. Abed, H. O. Wang, and R. C. Chen, Physica D 70, 154 (1994).
  39. W. Just, T. Bernard, M. Ostheimer, E. Reibold, and H. Benner, Phys. Rev. Lett. 78, 203 (1997).
  40. M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997).
  41. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Sec. 7.6.1.
  42. Analog Devices, One Technology Way, P.O. Box 9106, Norwood, Massachusetts 02062–9106.
  43. Press-n-Peel film ]100PNPR, Techniks, Inc., P. O. Box 463, Ringoes, New Jersey 08551.
  44. Andrew Corporation, 10500 W. 153rd Street, Orland Park, Illinois 60462.
  45. Hewlett-Packard, 3000 Hanover Street, Palo Alto, California 94304–1185.
  46. Kay Elemetrics Corp., 12 Maple Avenue, P. O. Box 2025, Pine Brook, New Jersey 07058–2025.
  47. J. Perez and C. Jeffries, Phys. Lett. A 92, 82 (1982).
  48. C. Jeffries and C. Perez, Phys. Rev. A 26, 2117 (1982).
  49. R. Hilborn, Phys. Rev. A 31, 378 (1985).
  50. P. S. Linsay, Phys. Rev. Lett. 47, 1349 (1981).
  51. J. Testa, J. Perez, and C. Jeffries, Phys. Rev. Lett. 48, 714 (1982).
  52. R. W. Rollins and E. R. Hunt, Phys. Rev. Lett. 49, 1295 (1982).
  53. E. R. Hunt and R. W. Rollins, Phys. Rev. A 29, 1000 (1984).
  54. Z. Su, R. W. Rollins, and E. R. Hunt, Phys. Rev. A 40, 2698 (1989).
  55. Tektronix, Inc., 26600 SW Parkway, P.O. Box 1000, Wilsonville, Oregon 97070–1000.
  56. A. Chang, G. M. Hall, J. R. Gardner and D. J. Gauthier (preprint).
  57. T. C. Newell, P. M. Alsing, A. Gavrielides, and V. Kovanis, Phys. Rev. E 51, 2963 (1995).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics