ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ponomarenko V. I., Prokhorov M. D., Karavaev A. S., Seleznev E. P., Dikanev T. V. Recovery of dynamical models of time-delay systems from time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 56-66. DOI: 10.18500/0869-6632-2003-11-3-56-66

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Language: 
English
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/0869-6632-2003-11-3-56-66

Recovery of dynamical models of time-delay systems from time series

Autors: 
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Karavaev Anatolij Sergeevich, Saratov State University
Seleznev Evgeny Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Dikanev Taras Viktorovich, Huawei Technologies Co in Russia
Abstract: 

We develop the method for the estimation оf the parameters оf time-delay systems from time series. The method is based on the statistical analysis of time intervals between extrema in the time series and the projection of the infinite-dimensional phase space оf а time-delay system to suitably chosen low-dimensional subspaces. We verify our method by using it for the reconstruction оf different time-delay differential equations from their chaotic solutions.

Key words: 
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Acknowledgments: 
The authors thank B.P. Bezruchko for stimulating discussions. This work was supported by the Russian Foundation о Fundamental Research, Grant № 03-02-17593, U.S. Civilian Research Development Foundation for the Independent States of the Former Soviet Union, Award № REC-006, State contract M 40.020.1.1.1168 with Minpromnauki RF, аnd FNP «Dynasty» аnd ICFFM, Grant № 245 662.
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Received: 
04.09.2003
Accepted: 
02.11.2003
Available online: 
23.11.2023
Published: 
31.12.2003
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