For citation:
Cherepantsev A. S. Effect of filtering in dynamic system parameters estimation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 6, pp. 47-55. DOI: 10.18500/0869-6632-2012-20-6-47-55
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 163)
Language:
Russian
Heading:
Article type:
Article
UDC:
517.9 + 519.254
Effect of filtering in dynamic system parameters estimation
Autors:
Cherepantsev Aleksandr Sergeevich, Southern Federal University. Faculty of Natural Science and Humanities Education
Abstract:
A question on the distortion of the dynamic system parameters estimation using a time variation of the single component after exposing recursive filters with different order and with different cut-off frequency is analyzed. The Lorenz system is used as a test dynamic system for comparative evaluation of the correlation dimension and the dimension of the system state vector in the case of recursive filtering.
Reference:
- Malinetskii GG, Potapov AB. Modern Problems of Nonlinear Dynamics. Moscow: Editorial URSS; 2002. 360 p. (in Russian).
- Badii R, Broggi G, Derighetti B et al. Dimension increase in filtered chaotic signals. Physical Review Letters. 1988;60(11):979–982. DOI: 10.1103/PhysRevLett.60.979.
- Kaplan JL, Yorke JA. Chaotic behavior of multidimensional difference equations. Functional differential equations and approximations of fixed points. In: Peitgen HO, Walther HO, editors. Lecture Notes in Mathematics. Vol. 730. Berlin: Springer-Verlag; 1979. P. 204–227. DOI: 10.1007/BFb0064319.
- Kuznetsov SP. Dynamic Chaos. Moscow: Fizmatlit; 2001. 295 p. (in Russian).
- Zhu L, Lai Y, Hoppensteadt F et al. Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics. Chaos. 2003;13(1):410–419. DOI: 10.1063/1.1520090.
- Broomhead D, Huke J, Muldoon M. Linear filters and non-linear systems. Journal Royal Statistical Society. 1992;54(2):373–382.
- Sauer T, Yorke J. Are the dimensions of a set and its image equal under typical smooth functions? Ergodic Theory and Dynamical Systems. 1997;17(4):941–956. DOI: 10.1017/S0143385797086252.
- Otnes RK, Enochson L. Applied Time Series Analysis. Vol. 1. Basic Techniques. New York: Wiley; 1978. 450 p.
- Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from chaotic signal. Physical Review A. 1983;28(4):2591–2593. DOI: 10.1103/PhysRevA.28.2591.
Received:
12.09.2012
Accepted:
30.10.2012
Published:
29.03.2013
Journal issue:
Short text (in English):
(downloads: 76)
- 2004 reads