International Journal of Computer
Trends and Technology

Research Article | Open Access | Download PDF

Volume 6 | Number 2 | Year 2013 | Article Id. IJCTT-V6N3P128 | DOI : https://doi.org/10.14445/22312803/IJCTT-V6N3P128

Reconstruction Models for Attractors in the Technical and Economic Processes

E.V. Nikulchev

Citation :

E.V. Nikulchev, "Reconstruction Models for Attractors in the Technical and Economic Processes," International Journal of Computer Trends and Technology (IJCTT), vol. 6, no. 2, pp. 171-175, 2013. Crossref, https://doi.org/10.14445/22312803/IJCTT-V6N3P128

Abstract

The article discusses building models based on the reconstructed attractors of the time series. Discusses the use of the properties of dynamical chaos, namely to identify the strange attractors structure models. Here is used the group properties of differential equations, which consist in the symmetry of particular solutions. Examples of modeling engineering systems are given.

Keywords

Chaotic Dynamics, Symmetry, Identification, Groups of transformations, reconstructed attractors, global reconstruction.

References

[1] F. Takens, Detecting Strange Attractors in Turbulence, in D. Rand and L.-S Young (Ed), Lecture notes in Mathematics, v.898, (Springer, 1981) 366-381.
[2] N.J. Packard, J.P. Crutchfield, J.D. Fromer and R.S. Shaw, Geometry from a Time-Series, Phys. Rev. Letters, 45(9), 1980, 712.
[3] R. Brawn, N. F. Rulkov and E. R. Tracy, Modelling and synchronizing chaotic systems from time-series data, Pthys. Rev. E. 49, 1994, 3784.
[4] J.L. Breeden and A. Hubler, Reconstructing equations of motion from experimental data with unobserved variables, Phys. Rev. A. 42(10), 1990, 5817.
[5] N.В. Janson, A.N. Pavlov, 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 (NJ: Nova Science publishers, 2003), 287–317.
[6] U.S. Freitas, C. Letellier, and L. A. Aguirre, Failure in distinguishing colored noise from chaos using the “noise titration” technique, Phys. Rev. E, 79(3), 2009, 35201.
[7] C. Tao, X. Liu, and J.J. Jiang, Global modeling of complex data series using the term-ranking approach and its application to voice synthesis, Phys. Rev. E, 84(2), 2011. 26205.
[8] C.a. Letellier and L.A.b. Aguirre, Dynamical analysis of fractional-order Rössler and modified Lorenz systems. Phys. Let. A. 377 (28-30), 2013, 1707 (doi: 10.1016/j.physleta.2013.05.006)
[9] L.F.P. Franca and M.A. Savi, Estimating Attractor Dimension on the Nonlinear Pendulum Time Series, Journal of the Brazilian Society of Mechanical Sciences, 23(4), 2001. (doi: 10.1590/S0100-73862001000400004)
[10] L. A. Aguirre and C. Letellier, Modeling Nonlinear Dynamics and Chaos: A Review, Mathematical Problems in Engineering, V.2009. (doi: 10.1155/2009/238960)
[11] E.V. Nikulchev, Geometric method of reconstructing systems from experimental data, Technical Physics Letters,33(3), 2007, 267.
[12] Z. Liu Chaotic Time Series Analysis, Mathematical Problems in Engineering. V.2010. (doi:10.1155/2010/720190)
[13] E. Nikulchev and Kozlov O. Identification of Structural Model for Chaotic Systems, Journal of Modern Physics, 4(10), 2013, 1381. (doi: 10.4236/jmp.2013.410166)
[14] D.O. Ledenyov and V.O. Ledenyov, On the optimal allocation of assets in investment portfolio with application of modern portfolio management and nonlinear dynamic chaos theories in investment, commercial and central banks, Cornell University NY USA www.arxiv.org 1301.4881.pdf. [15] T. Mokritskaya, The phase portrait and degradation in soil International Journal of Engineering Science Invention, 2(4), 2013, 27.
[16] A.G. Miski-Oglu, N.S. Shlapak and O.V. Goroshko, Modern intelligent methods in managing the organization // Proc. «Nauka i studia»,  2012, http://www.rusnauka.com/ 27_SSN_2012/Economics/6_116214.doc.htm
[17] L. Ljung, System Identification Toolbox for Use with MATLAB. Mathwork Inc., 2007.
[18] E.V. Pluzhnik and E.V. Nikulchev, Use of Dynamical Systems Modeling to Hybrid Cloud Database Int'l J. of Communications, Network and System Sciences, 6(12), 2013, 505. (doi: 10.4236/ijcns.2013.612054).