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Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser

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Zeitschrift für Physik B Condensed Matter

Abstract

Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certainanholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.

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References

  1. Zeghlache, H., Mandel, P., Abraham, N.B., Weiss, C.O.: Phys. Rev.38A, 3128 (1988)

    Google Scholar 

  2. Tarroja, M.F.H., Abraham, N.B., Bandy, D.K., Narducci, L.M.: Phys. Rev.34 A, 3148 (1986)

    Google Scholar 

  3. Fowler, A.C., Gibbon, J.D., McGuinness, M.J.: Physica7D, 126 (1983),4D, 139 (1982);

    Google Scholar 

  4. Gibbon, J.D., McGuinness, M.J.: Physica5D, 108 (1982)

    Google Scholar 

  5. Ning, C.Z., Haken, H.: Phys. Rev. A41, 3826 (1990)

    Google Scholar 

  6. Mandel, P., Zeglache, H.: Opt. Commun.47, 146 (1983);

    Google Scholar 

  7. Zeghlache, H., Mandel, P.: J. Opt. Sci. Am.2B, 18 (1985)

    Google Scholar 

  8. Haken, H.: Synergetics. An introduction. 3rd Edn. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  9. Haken, H.: Advanced synergetics. 2nd Edn. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  10. Ning, C.Z.: J. Phys. A Math. Gen.21, L491 (1988)

    Google Scholar 

  11. Risken, H., Nummedal, K.: J. Appl. Phys.39, 4662 (1968)

    Google Scholar 

  12. Graham, R.: Phys. Lett.58A, 440 (1976)

    Google Scholar 

  13. Berry, M.V.: Proc. R. Soc. A392, 45 (1984); J. Phys. A Math. Gen.18, 15 (1985), Nature326, 277 (1987); Sci. Am. (Dec. 1988)

    Google Scholar 

  14. Hannay, J.H.: J. Phys. A Math Gen.18, 221 (1985)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57/4, D-7000, Stuttgart 80, Federal Republic of Germany

    Cun-Zheng Ning & Hermann Haken

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  1. Cun-Zheng Ning
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  2. Hermann Haken
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Ning, CZ., Haken, H. Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser. Z. Physik B - Condensed Matter 81, 457–461 (1990). https://doi.org/10.1007/BF01390829

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  • DOI: https://doi.org/10.1007/BF01390829

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