Identification of chaotic systems with hidden variables (modified Bock's algorithm)

被引:17
作者
Bezruchko, BP
Smirnov, DA
Sysoev, IV
机构
[1] Saratov NG Chernyshevskii State Univ, Dept Elect Oscillat & Waves, Saratov 410026, Russia
[2] Russian Acad Sci, Inst Radioengn & Elect, Saratov Branch, Saratov 410019, Russia
基金
俄罗斯基础研究基金会;
关键词
D O I
10.1016/j.chaos.2005.08.204
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We address the problem of estimating parameters of chaotic dynamical systems from a time series in a situation when some of state variables are not observed and/or the data are very noisy. Using specially developed quantitative criteria, we compare performance of the original multiple shooting approach (Bock's algorithm) and its modified version. The latter is shown to be significantly superior for long chaotic time series. In particular, it allows to obtain accurate estimates for much worse starting guesses for the estimated parameters. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码:82 / 90
页数:9
相关论文
共 27 条
[1]  
BAAKE E, 1992, B MATH BIOL, V54, P999
[2]   FITTING ORDINARY DIFFERENTIAL-EQUATIONS TO CHAOTIC DATA [J].
BAAKE, E ;
BAAKE, M ;
BOCK, HG ;
BRIGGS, KM .
PHYSICAL REVIEW A, 1992, 45 (08) :5524-5529
[3]  
Bock H., 1981, SPRINGER SERIES CHEM, P102
[4]   Markov chain Monte Carlo estimation of nonlinear dynamics from time series [J].
Bremer, CL ;
Kaplan, DT .
PHYSICA D-NONLINEAR PHENOMENA, 2001, 160 (1-2) :116-126
[5]  
BUTKOVSKII OY, 2002, RADIOPHYS QUANT EL, V45, P55
[6]  
Gouesbet G, 2003, CHAOS AND ITS RECONSTRUCTION, P1
[7]   GLOBAL VECTOR-FIELD RECONSTRUCTION BY USING A MULTIVARIATE POLYNOMIAL L(2) APPROXIMATION ON NETS [J].
GOUESBET, G ;
LETELLIER, C .
PHYSICAL REVIEW E, 1994, 49 (06) :4955-4972
[8]   Dynamical properties of a ferroelectric capacitor observed through nonlinear time series analysis [J].
Hegger, R ;
Kantz, H ;
Schmuser, F ;
Diestelhorst, M ;
Kapsch, RP ;
Beige, H .
CHAOS, 1998, 8 (03) :727-736
[9]   Asymptotic scaling laws for precision of parameter estimates in dynamical systems [J].
Horbelt, W ;
Timmer, J .
PHYSICS LETTERS A, 2003, 310 (04) :269-280
[10]   Identifying physical properties of a CO2 laser by dynamical modeling of measured time series -: art. no. 016222 [J].
Horbelt, W ;
Timmer, J ;
Bünner, MJ ;
Meucci, R ;
Ciofini, M .
PHYSICAL REVIEW E, 2001, 64 (01) :7