Skip to main content
Log in

Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers

I. The Lorenz system in the simplest quantum laser model and application to it of the method of averaging

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

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.

Literature Cited

  1. E. N. Lorenz, J. Atmos. Sci.,20, 130 (1963).

    Google Scholar 

  2. A. N. Oraevskii, Kvantovaya Elektron. (Moscow),8, 130 (1981).

    Google Scholar 

  3. H. Haken, Phys. Lett. A,53, 77 (1975).

    Google Scholar 

  4. G. M. Zaslavskii, Statistical Irreversibility in Nonlinear Systems [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  5. A. A. Bunimovich and Ya. G. Sinai, “Stochasticity of the attractor in the Lorenz model,” in: Nonlinear Waves [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  6. Strange Attractors [Russian translations], Mir, Moscow (1981).

  7. M. I. Rabinovich, Usp. Fiz. Nauk,125, 123 (1978).

    Google Scholar 

  8. A. V. Gaponov-Grekhov and M. I. Rabinovich, Usp. Fiz. Nauk,128, 579 (1979).

    Google Scholar 

  9. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, Dokl. Akad. Nauk SSSR,234, 336 (1977).

    Google Scholar 

  10. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, Tr. Mosk. Mat. Ob.,44, 150 (1982).

    Google Scholar 

  11. L. P. Shil'nikov, “Bifurcation theory and the Lorenz model,” Supplement II to the Russian translation of: J. Marsden and M. F. McCracken, The Hopf Bifurcation and its Applications translation published by Mir, Moscow (1980).

    Google Scholar 

  12. N. N. Bogolyubov and Yu. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).

    Google Scholar 

  13. N. N. Bogolyubov and D. N. Zubarev, Ukr. Mat. Zh.,7, 5 (1955).

    Google Scholar 

  14. N. N. Bogolyubov, “Problems of a dynamical theory in statistical physics,” in: Studies in Statistical Mechanics, Vol. 1 (eds. J. de Boer and G. E. Uhlenbeck), North-Holland, Amsterdam (1962).

    Google Scholar 

  15. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, Plenum, New York (1974).

    Google Scholar 

  16. A. N. Oraevskii, Molecular Generators [in Russian], Nauka, Moscow (1964).

    Google Scholar 

  17. J. P. Gordon, Phys. Rev.,161, 367 (1967).

    Google Scholar 

  18. H. Haken, Handbuch der Physik, Springer, Berlin (1970).

    Google Scholar 

  19. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, Wiley, New York (1975).

    Google Scholar 

  20. Yu. L. Klimontovich, Kinetic Theory of Electromagnetic Processes [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  21. K. A. Robbins, SIAM J. Appl. Math.,36, 457 (1979).

    Google Scholar 

  22. J. A. Yorke and E. Yorke, “Metastable chaos;” J. L. Kaplan and J. A. Yorke “Preturbulence,” in: Strange Attractors [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  23. L. A. Pokrovskii, Teor. Mat. Fiz.,37, 102 (1978).

    Google Scholar 

  24. L. A. Pokrovskii and A. M. Khazanov, Teor. Mat. Fiz.,50, 146 (1982).

    Google Scholar 

  25. L. A. Pokrovsky, Physica (Utrecht),105, 105 (1981).

    Google Scholar 

  26. A. A. Andronov, A. A. Vitt, and C. E. Khaikin, Theory of Oscillators, Pergamon Press, Oxford (1966).

    Google Scholar 

  27. J. Marsden and M. McCracken, The Hopf Bifurcation and its Applications, Springer, New York (1976).

    Google Scholar 

  28. N. N. Bautin and L. P. Shil'nikov, Supplement I to Russian translation of [27] published by Mir, Moscow (1980).

    Google Scholar 

  29. N. V. Roshchin, Prikl. Mat. Mekh.,5, 950 (1978).

    Google Scholar 

  30. M. A. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions [Russian translation], Nauka, Moscow (1979).

    Google Scholar 

Download references

Authors

Additional information

All-Union Scientific Research Center for Study of Surface and Vacuum Properties. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 62, No. 2, pp. 272–290, February, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pokrovskii, L.A. Solution of the system of Lorenz equations in the asymptotic limit of large Rayleigh numbers. Theor Math Phys 62, 183–196 (1985). https://doi.org/10.1007/BF01033529

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01033529

Keywords

Navigation