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Ponomarenko V. I., Prokhorov M. D. Reconstruction of time-delay systems equations over experimental time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 52-64. DOI: 10.18500/0869-6632-2002-10-1-52-64

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Reconstruction of time-delay systems equations over experimental time series

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

We propose а new method to reconstruct the time-delay differential equations over time series. The method is based on extreme location in the time series. On the base of information about time delay we determine nonlinear function and inertiality parameter. We verify our method by using it for the reconstruction of the time-delay differential equations from their chaotic solutions and for modelling experimental systems with delay-induced dynamics from their chaotic time series. 

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This work was supported by the Russian Foundation for Basic Research (grant No. 02-02-17578), Young Scientists Grant No. 23 RAS, and CRDF grant REC-006.
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