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Experimental observation of dynamics near the torus-doubling terminal critical point

Boris P. Bezruchko1,2, Sergey P. Kuznetsov1, and Yevgeniy P. Seleznev1

  • 1Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Saratov Branch, 38, Zelyonaya Street, Saratov 410019, Russia
  • 2Department of Physics, Saratov State University, 83, Astrakhanskaya Street, Saratov 410026, Russia

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Phys. Rev. E 62, 7828 – Published 1 December, 2000

DOI: https://doi.org/10.1103/PhysRevE.62.7828

Abstract

A nonlinear electronic circuit driven by two signals with golden mean frequency ratio is studied. We have observed different dynamical regimes, including tori, doubled tori, strange nonchaotic attractors, and chaos, which all meet together at the critical point terminating the torus-doubling bifurcation curve (TDT point) in the parameter plane of the system. The parameter plane arrangement, spectra, and portraits of attractors observed in the experiment are in reasonable coincidence with numerical computations for a quasiperiodically forced logistic map, where the TDT critical point originally has been found and studied theoretically [S. Kuznetsov, A. Pikovsky, and U. Feudel, Phys. Rev. E 57, 1585 (1998)].

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References (26)

  1. C. Grebogi, E. Ott, S. Pelikan, and J.A. Yorke, Physica D 13, 261 (1984).
  2. F.J. Romeiras, A. Bondeson, E. Ott, T.M. Antonsen, and C. Grebogi, Physica D 26, 277 (1987).
  3. F.J. Romeiras and E. Ott, Phys. Rev. A 35, 4404 (1987).
  4. M. Ding, C. Grebogi, and E. Ott, Phys. Rev. A 39, 2593 (1989).
  5. T. Kapitank, E. Ponce, and J. Wojewoda, J. Phys. A 23, L383 (1990).
  6. A. Pikovsky and U. Feudel, Chaos 5, 253 (1995).
  7. U. Feudel, J. Kurths, and A. Pikovsky, Physica D 88, 176 (1995).
  8. W.L. Ditto et al., Phys. Rev. Lett. 65, 533 (1990).
  9. T. Zhou, F. Moss, and A. Bulsara, Phys. Rev. A 45, 5394 (1992).
  10. J.F. Heagy and S.M. Hammel, Physica D 70, 140 (1994).
  11. S. Kuznetsov, A. Pikovsky, and U. Feudel, Phys. Rev. E 51, R1629 (1995).
  12. Y.-C. Lai, Phys. Rev. E 53, 57 (1996).
  13. T. Nishikawa and K. Kaneko, Phys. Rev. E 54, 6114 (1996).
  14. V.S. Anishchenko, T.E. Vadivasova, and O.N. Sosnovtseva, Phys. Rev. E 53, 4451 (1996).
  15. S. Kuznetsov, A. Pikovsky, and U. Feudel, Phys. Rev. E 57, 1585 (1998).
  16. M.J. Feigenbaum, J. Stat. Phys. 19, 25 (1978).
  17. M.J. Feigenbaum, L.P. Kadanoff, and S.J. Shenker, Physica D 5, 370 (1982).
  18. D. Rand, S. Ostlund, J. Sethna, and E.D. Siggia, Physica D 8, 303 (1983).
  19. K. Kaneko, Prog. Theor. Phys. 69, 1806 (1983).
  20. A. Arneodo, Phys. Rev. Lett. 53, 1240 (1984).
  21. S.P. Kuznetsov, Zh. Éksp. Teor. Fiz. 39, 113 (1984) [JETP Lett. 39, 133 (1984)].
  22. A. Arneodo, P.H. Collet, and E.A. Spiegel, Phys. Lett. A 94, 1 (1983).
  23. V. S. Anishchenko. Dynamical Chaos—Models and Experiments (World Scientific, Singapore, 1995).
  24. P.S. Linsay, Phys. Rev. Lett. 47, 1349 (1981).
  25. J. Testa, J. Perez, and C. Jeffries, Phys. Rev. Lett. 48, 714 (1982).
  26. V.V. Astakhov, B.P. Bezruchko, Ye.P. Seleznev, Radiotekh. Elektron. (Moscow) 32, 2558 (1987).

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Phys. Rev. E 62, 7828– Published 1 December, 2000
  • Received 10 February 2000

© 2000 American Physical Society

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