Skip to main content
Log in

Chaotic synchronization of unidirectionally coupled electron-wave media with interacting counterpropagating waves

  • Theoretical and Mathematical Physics
  • Published:
Technical Physics Aims and scope Submit manuscript

Abstract

Chaotic synchronization of two electron-wave media with interacting counterpropagating waves and cubic phase nonlinearity (transverse-field backward-wave oscillators) is studied. Analysis is based on considering a continuous set of the phases of a chaotic signal. The parameters of chaotic synchronization in a system of unidirectionally coupled backward-wave oscillators are found, and the complex dynamics of establishing the chaotic synchronization conditions in an active medium is investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).

    Article  ADS  Google Scholar 

  2. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: Universal Concept in Nonlinear Sciences (Cambridge Univ. Press, Cambridge, 2001).

    Google Scholar 

  3. C. M. Ticos, E. Rosa, W. B. Pardo, et al., Phys. Rev. Lett. 85, 2929 (2000).

    Article  ADS  Google Scholar 

  4. V. A. Anishenko, A. G. Balanov, N. B. Janson, et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 2339 (2000).

    Google Scholar 

  5. P. A. Tass et al., Phys. Rev. Lett. 90, 088101 (2003).

  6. M. D. Prokhorov et al., Phys. Rev. E 68, 041913 (2003).

  7. A. S. Dmitriev and A. I. Panas, Dynamic Chaos: Advanced Data Carries for Communications (Fizmatlit, Moscow, 2002) [in Russian].

    Google Scholar 

  8. A. A. Koronovskii, D. I. Trubetskov, and A. E. Hramov, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 45, 773 (2002).

    Google Scholar 

  9. D. I. Trubetskov and A. E. Hramov, Radiotekh. Élektron. (Moscow) 48, 116 (2003).

    Google Scholar 

  10. N. M. Ryskin and V. N. Titov, Zh. Tekh. Fiz. 73(9), 90 (2003) [ Tech. Phys. 48, 1170 (2003)].

    Google Scholar 

  11. V. S. Anishchenko and T. E. Vadivasova, Radiotekh. Élektron. (Moscow) 47, 133 (2002).

    Google Scholar 

  12. A. Pikovsky, M. Rosenblum, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 2291 (2000).

    Article  MathSciNet  Google Scholar 

  13. V. S. Anishchenko and T. E. Vadivasova, Radiotekh. Élektron. (Moscow) 49, 123 (2004).

    Google Scholar 

  14. A. A. Koronovskii and A. E. Hramov, Pis’ma Zh. Éksp. Teor. Fiz. 79, 391 (2004) [JETP Lett. 79, 316 (2004)].

    Google Scholar 

  15. Wavelets in Physics, Ed. by J. C. van den Berg (Cambridge Univ. Press, Cambridge, 1998).

    Google Scholar 

  16. A. A. Koronovskii and A. E. Hramov, Continuous Wavelet Analysis and Its Applications (Fizmatlit, Moscow, 2003) [in Russian].

    Google Scholar 

  17. D. I. Trubetskov and A. E. Hramov, Lectures on Microwave Electronics for Physicists (Fizmatlit, Moscow, 2003), Vol. 1 [in Russian].

    Google Scholar 

  18. A. P. Chetverikov, Izv. Akad. Nauk, Ser. Fiz. 58, 171 (1994).

    Google Scholar 

  19. A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 10, 1415 (1967).

    Google Scholar 

  20. S. P. Kuznetsov and A. P. Chetverikov, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 109 (1981).

    Google Scholar 

  21. A. P. Chetverikov, Vyssh. Uchebn. Zaved. Prikl. Nelin. Din. 2(5), 46 (1994).

    Google Scholar 

  22. J. Kurths and A. S. Pikovsky, Chaos, Solitons and Fractals 5, 1893 (1995).

    Article  Google Scholar 

  23. F. Takens, Lectures Notes in Mathematics, Ed. by D. Rand and L.-S. Young (Springer, New York, 1981).

    Google Scholar 

  24. A. A. Koronovskii, D. I. Trubetskov, and A. E. Hramov, Dokl. Akad. Nauk 395, 143 (2004) [Dokl. Phys. 49, 143 (2004)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 75, No. 4, 2005, pp. 1–10.

Original Russian Text Copyright © 2005 by Koronovskii, Popov, Hramov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koronovskii, A.A., Popov, P.V. & Hramov, A.E. Chaotic synchronization of unidirectionally coupled electron-wave media with interacting counterpropagating waves. Tech. Phys. 50, 385–393 (2005). https://doi.org/10.1134/1.1901774

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1901774

Keywords

Navigation