Geodesic
Nonlinear signal reconstruction based on the decomposition into chaotic components
Journal of computational and engineering mathematics, Tome 4 (2017) no. 4, pp. 29-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper proposes a signal reconstruction technique based on the decomposition into chaotic components. The considered approach can be usefully associated with the filtering, forecasting and control algorithms when only a small number of data samples is available. The developed decomposition algorithm involves sequential component extraction and recursive computation of the cost function. Some related questions are also discussed: choice of the class of chaotic maps, computational complexity of parameter estimation.
Keywords: signal reconstruction, chaotic map, parameter estimation, multiextremal cost function. 
@article{JCEM_2017_4_4_a2,
     author = {A. S. Sheludko},
     title = {Nonlinear signal reconstruction based on the decomposition into chaotic components},
     journal = {Journal of computational and engineering mathematics},
     pages = {29--37},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2017_4_4_a2/}
}
TY  - JOUR
AU  - A. S. Sheludko
TI  - Nonlinear signal reconstruction based on the decomposition into chaotic components
JO  - Journal of computational and engineering mathematics
PY  - 2017
SP  - 29
EP  - 37
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2017_4_4_a2/
LA  - en
ID  - JCEM_2017_4_4_a2
ER  - 
%0 Journal Article
%A A. S. Sheludko
%T Nonlinear signal reconstruction based on the decomposition into chaotic components
%J Journal of computational and engineering mathematics
%D 2017
%P 29-37
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2017_4_4_a2/
%G en
%F JCEM_2017_4_4_a2
A. S. Sheludko. Nonlinear signal reconstruction based on the decomposition into chaotic components. Journal of computational and engineering mathematics, Tome 4 (2017) no. 4, pp. 29-37. http://geodesic.mathdoc.fr/item/JCEM_2017_4_4_a2/

[1] L. A. Aguirre, C. Letellier, “Modeling Nonlinear Dynamics and Chaos: A Review”, Mathematical Problems in Engineering, 2009 (2009) | DOI | MR

[2] B. P. Bezruchko, D. A. Smirnov, Extracting Knowledge From Time Series. An Introduction to Nonlinear Empirical Modeling, Springer, Berlin, Heidelberg, 2010 | DOI | MR | Zbl

[3] J. M. T. Thompson, “Extracting Knowledge From Time Series. An Introduction to Nonlinear Empirical Modeling”, International Journal of Bifurcation and Chaos, 26:13 (2016) | DOI

[4] N. K. Vitanov, K. Sakai, Z. I. Dimitrova, “SSA, PCA, TDPSC, ACFA: Useful Combination of Methods for Analysis of Short and Nonstationary Time Series”, Chaos, Solitons Fractals, 37:1 (2008), 187–202 | DOI

[5] L. Ljung, “Perspectives on System Identification”, Annual Reviews in Control, 34:1 (2010), 1–12 | DOI | MR

[6] J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, 2003 | MR | Zbl

[7] V. I. Shiryaev, E. O. Podivilova, “Set-valued Estimation of Linear Dynamical System State When Disturbance is Decomposed as a System of Functions”, Procedia Engineering, 129 (2015), 252–258 | DOI

[8] E. I. Malyutina, V. I. Shiryaev, “Time Series Forecasting Using Nonlinear Dynamic Methods and Identification of Deterministic Chaos”, Procedia Computer Science, 31 (2014), 1022–1031 | DOI

[9] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Westview Press, 1989 | MR | Zbl

[10] M. M. Dubovikov, N. V. Starchenko, M. S. Dubovikov, “Dimension of the Minimal Cover and Fractal Analysis of Time Series”, Physica A, 339 (2004), 591–608 | DOI | MR

[11] V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, G. I. Strelkova, “Correlation Analysis of Dynamical Chaos”, Physica A, 325 (2003), 199–212 | DOI | MR | Zbl

[12] A. Erramilli, R. P. Singh, P. Pruthi, “An Application of Deterministic Chaotic Maps to Model Packet Traffic”, Queueing Systems, 20 (1995), 171–206 | DOI | MR | Zbl

[13] M. A. Jafarizadeh, S. Behnia, S. Khorram, H. Nagshara, “Hierarchy of Chaotic Maps with an Invariant Measure”, Journal of Statistical Physics, 104 (2001), 1013–1028 | DOI | MR | Zbl

[14] S. Jafari, V.-T. Pham, S. M. R. H. Golpayegani et al., “The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors”, International Journal of Bifurcation and Chaos, 26:13 (2016) | DOI | MR

[15] A. A. Kipchatov, E. L. Kozlenko, “Reconstruction of Chaotic Oscillations After Passage Through Linear Filters”, Technical Physics Letters, 25:2 (1999), 148–150 | DOI

[16] D. Simon, Optimal State Estimation: Kalman, H-infinity, and Nonlinear Approaches, Wiley, Hoboken, NJ, 2006

[17] A. Banerjee, I. Abu-Mahfouz, “Comparative Analysis of Particle Swarm Optimization and Differential Evolution Algorithms for Parameter Estimation in Nonlinear Dynamic Systems”, Chaos, Solitons Fractals, 58 (2014), 65–83 | DOI | MR | Zbl

[18] Y. Jiang, F. C. M. Lau, S. Wang, C. K. Tse, “Parameter Identification of Chaotic Systems by a Novel Dual Particle Swarm Optimization”, International Journal of Bifurcation and Chaos, 26:2 (2016) | DOI | MR

[19] A. Gotmare, S. S. Bhattacharjee, R. Patidar, N. V. George, “Swarm and Evolutionary Computing Algorithms for System Identification and Filter Design: A Comprehensive Review”, Swarm and Evolutionary Computation, 32 (2017), 68–84 | DOI