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Identification of Structural Model for Chaotic Systems

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DOI: 10.4236/jmp.2013.410166    4,068 Downloads   5,583 Views   Citations

ABSTRACT

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the basis of the attractors which can be identified and the mere sight of models. It is known that the knowledge of the symmetry group allows you to specify the form of a minimal system. Forming a group transformation can be found in the reconstructed attractor. The affine system as the basic model is selected. Type of a nonlinear system is the subject of calculations. A theoretical analysis is performed and proof of the possibility of constructing models in the central invariant manifold reduced. This developed algorithm for determining the observed symmetry in the attractor. The results of identification used in real systems are an application.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

E. Nikulchev and O. Kozlov, "Identification of Structural Model for Chaotic Systems," Journal of Modern Physics, Vol. 4 No. 10, 2013, pp. 1381-1392. doi: 10.4236/jmp.2013.410166.

References

[1] N. H. Packard, J. P. Crutchfield, J. D. Farmer and S. Shaw, Physical Review Letters, Vol. 45, 1980, pp. 712-716. http://dx.doi.org/10.1103/PhysRevLett.45.712
[2] F. Detecting, Lecture Notes in Mathematics, Vol. 898, 1980, pp. 366-381.
[3] X. Cremers and А. Hubler, Verlag der Zeitschrift für Naturforschung, Vol. 42, 1987, pp. 797-802.
[4] J. P Crutchfield and B. S. McNamara, Complex Systems, Vol. 1, 1987, pp. 417-452.
[5] N. В. Janson, A. N. Pavlov and V. S. Anisliclienko, “Global Reconstruction: Application to Biological Data and Secure Communication,” In: G. Gouesbet and S. Meunier-Guttin-Cluzel, Ed., Chaos and Its Reconstruction, Nova Science Publishers, New York, 2003, pp. 287-317.
[6] L. A. Aguirre and E. M. Mendes, International Journal of Bifurcation and Chaos, Vol. 6, 1996, pp. 279-294.
http://dx.doi.org/10.1142/S0218127496000059
[7] L. A. Aguirre and S. A. Billings, Physica D, Vol. 85, 1995, pp. 239-258.
http://dx.doi.org/10.1016/0167-2789(95)00116-L
[8] L. Cao, Physica D, Vol. 110, 1997, pp. 43-50.
http://dx.doi.org/10.1016/S0167-2789(97)00118-8
[9] G. Gouesbet and X. Maquet, Physica D, Vol. 58, 1992, pp. 202-215.
http://dx.doi.org/10.1016/0167-2789(92)90109-Z
[10] M. T. Rosenstein, J. J. Collins and C. J. De Luca, Physica D, Vol. 73, 1994, pp. 82-98.
http://dx.doi.org/10.1016/0167-2789(94)90226-7
[11] T. Sauer, Physical Review Letters, Vol. 72, 1994, pp. 3811-3814.
http://dx.doi.org/10.1103/PhysRevLett.72.3811
[12] R. Brawn, N. F. Rulkov and E. R. Tracy, Physical Review E, Vol. 49, 1994, pp. 3784-3800.
http://dx.doi.org/10.1103/PhysRevE.49.3784
[13] J. L. Breeden and A. Hubler, Physical Review A, Vol. 42, 1990, pp. 5817-5826.
http://dx.doi.org/10.1103/PhysRevA.42.5817
[14] G. Gouesbet and С. Letellier, Physical Review E, Vol. 49, 1994, pp. 4955-4972.
[15] L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev and L. O. Chu, “Methods of Qualitative Theory in Nonlinear Dynamics. Part 1, 2,” World Scientific Publishing, Singapore City, 1998.
[16] B. Hasselblatt and A. Katok, “A First Course in Dynamics—With a Panorama of Recent Developments,” Cambridge University Press, Cambridge, 2003.
[17] E. V. Nikulchev, Technical Physics Letters, Vol. 33, 2007, pp. 267-269.
http://dx.doi.org/10.1134/S1063785007030248

  
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