Vol. 27, issue 01, article # 1

Arsen'yan T. I., Grebennikov D. Yu., Sukhareva N. A., Sukhorukov A. P. Phase trajectories reconstruction for a laser beam propagated through a turbulent media. // Optika Atmosfery i Okeana. 2014. V. 27. No. 01. P. [in Russian].
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The instrument of phase trajectories and phase portraits is applied to the analysis of the fluctuation processes in the open space optical channels of data transmission. Experimental time series of intensity distributions in the detection plane were used to reconstruct the space of embedding dimension for the first two spatial moments. Knowledge of the structure of the phase trajectories reconstructed would allow one to predict the dynamics of spatial-temporal fluctuation processes for different time scales.


open space optical channel, space of embedding dimension, phase trajectory, turbulence


1. Hopf E. A mathematical example displaying features of turbulence // Commun. Pure and Appl. Math. 1948. N 1. P. 303–322.
2. Landau L.D., Lifshic E.M. Teoreticheskaja fizika. Gidrodinamika. V. 6. M.: Nauka, 1986. 736 p.
3. Ruelle D., Takens F. On the Nature of Turbulence // Commun. Math. Phys. 1971. N 20. P. 167–192.
4. Marsden J.E., McCraken M. The Hopf bifurkation and its applications // Appl. Math. Sci. Berlin: Springer-Verlag, 1976. N 19. 408 р.
5. Ruelle D. Turbulence, Strange Attractors and Chaos // World Scientific Series on Nonlinear Science Series. A. 1995. V. 16. 488 p.
6. Cohen L., Poor H.V., Scally M.O. (eds.) Classical, Semi-classical and Quantum Noise. DOI: 10.1007/978-1-4419-6624-73, © Springer, LLC 2012. 298 p.
7. Cohen L., Loughlin P. Dispersion, its effects and compensation // Physics of automatic target recognition / F. Sadjadi (ed.). V. 3. Berlin: Springer, 2007. P. 105–125.
8. Arsen'jan T.I., Suhareva N.A., Suhorukov A.P. Turbulentnye vozmushhenija lazernogo puchka v fazovom prostranstve // Vestn. MGU. Series. 3. 2014. N 1.
9. Cohen L. On a fundamental property of the Wigner distribution // 7IEE Trans. Acoust, Speech, Signal Procesing. 1987. V. 35. P. 559–561.
10. Shljajh V.P. Kvantovaja optika v fazovom prostranstve. M.: Fizmatlit, 2005. 760 p.
11. Takens F. Detecting Strange Attractors in Turbulence // Lecture Notes in Math. N.Y.: Springer, 1981. V. 898. P. 366–381.
12. Sauer T., Yorke J., Casdagli M. Embedology // J. Stat. Phys. 1991. V. 65, iss. 3–4. P. 579–616.
13. Deyle E.R., Sugihara G. Generalized Theorems for Nonlinear State Space Reconstruction // 2011, PLoS ONE 6(3): e18295. DOI: 10.1371/journal.pone.0018295.
14. Il'jashenko Ju.S. Attraktory i ih fraktal'naja razmernost'. M.: MCNMO, 2006. 18 p.
15. Fraser A.M., Swinney Y.L. Independent coordinates for strange attractors from mutual information // Phys. Rev. A. 1986. V. 33, iss. 2. P. 1134–1140.
16. Kennel B., Brown R., Abarbanel H.D.I. Determining embedding dimension for phase-space reconstruction using a geometrical construction // Phys. Rev. A. 1992. V. 45, iss. 6. P. 3403–3411.
17. Hong-guang M.A., Chong-zhao H.A.N. Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction // Frontiers of Electrical and Electronic Engineering in China. 2006. N 1. P. 111–114.
18. Paket statisticheskogo analiza R. URL: http://cran.r-project.org/
19. Biblioteka analiza haoticheskih vremennyh rjadov timeseriesChaos. URL: http://cran.r-project.org/web/packages/tseriesChaos/
20. Biblioteka otobrazhenija v fazovom prostranstve scatterplot3d. URL: http://cran.r-project.org/web/packages/scatterplot3d/
21. Arnol'd V.I. Obyknovennye differencial'nye uravnenija. M.: MCNMO, 2012. 344 p.
22. Arnol'd V.I. Geometricheskie metody v teorii obyknovennyh differencial'nyh uravnenij. 4-e izd. M.: MCNMO, 2012. 384 p.