Parameter estimation in nonlinear delayed feedback systems from noisy data

被引：54

作者：

Horbelt, W ^{[1
]}

Timmer, J ^{[1
]}

Voss, HU ^{[1
]}

机构：

[1] Univ Freiburg, Freiburger Zentrum Datenanal & Modellbildung, D-79104 Freiburg, Germany

来源：

PHYSICS LETTERS A | 2002年 / 299卷 / 5-6期

关键词：

parameter estimation; delay differential equation; multiple shooting; system identification; nonlinear delayed feedback system; Maekey-Glass system;

D O I：

10.1016/S0375-9601(02)00748-X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We propose a method for the estimation of parameters of nonlinear delayed feedback systems from a time series. Being based on the multiple shooting approach it is fairly robust against high levels of observation noise and yields precise parameter estimates. We evaluate its performance using simulated data of the Mackey-Glass equation and present an application to observed time series of an electronic circuit with time delay. (C) 2002 Elsevier Science B.V All rights reserved.

引用

页码：513 / 521

页数：9

共 23 条

[1]

[Anonymous], 1997, MATH MODELLING IMMUN

[2] DYNAMICS OF A CO2-LASER WITH DELAYED FEEDBACK - THE SHORT-DELAY REGIME [J].

ARECCHI, FT ;

GIACOMELLI, G ;

LAPUCCI, A ;

MEUCCI, R .

PHYSICAL REVIEW A, 1991, 43 (09) :4997-5004

[3] Pitfalls in parameter estimation for delay differential equations [J].

Baker, C ;

Paul, CAH .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1997, 18 (01) :305-314

[4] Modelling and analysis of time-lags in some basic patterns of cell proliferation [J].

Baker, CTH ;

Bocharov, GA ;

Paul, CAH ;

Rihan, FA .

JOURNAL OF MATHEMATICAL BIOLOGY, 1998, 37 (04) :341-371

[5] Reconstruction of time-delay systems from chaotic time series [J].

Bezruchko, BP ;

Karavaev, AS ;

Ponomarenko, VI ;

Prokhorov, MD .

PHYSICAL REVIEW E, 2001, 64 (05) :6-056216

[6] Numerical modelling in biosciences using delay differential equations [J].

Bocharov, GA ;

Rihan, FA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 125 (1-2) :183-199

[7]

Bock H. G., 1983, Progress in Scientific Computating, P95, DOI DOI 10.1007/978-1-4684-7324-77

[8] Tool to recover scalar time-delay systems from experimental time series [J].

Bunner, MJ ;

Popp, M ;

Meyer, T ;

Kittel, A ;

Parisi, J .

PHYSICAL REVIEW E, 1996, 54 (04) :R3082-R3085

[9] Analysis of an SEIRS epidemic model with two delays [J].

Cooke, KL ;

vandenDriessche, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1996, 35 (02) :240-260

[10] Mathematical modelling of the intravenous glucose tolerance test [J].

De Gaetano, A ;

Arino, O .

JOURNAL OF MATHEMATICAL BIOLOGY, 2000, 40 (02) :136-168

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