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Reconstruction of chaotic systems of a certain class

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Abstract

We use a scalar time series to find an unknown original system (OS) of ordinary differential equations in a given class. To solve this problem, we first construct a standard system (SS) of a known type having the observable and its derivatives as variables. Then we pass from the SS to the sought OS. To this end, we propose a new method that we call a method of perspective coefficients. It involves an analysis of relations between the coefficients of the OS, the SS, and the numerical values of the SS coefficients obtained for the studied time series. The method permits to obtain a number of OS’s that yield the given scalar time series. Here we recover exactly the observable variable rather than obtain its approximation. In some cases, using the proposed approach one can obtain a unique candidate system even if no additional information is available. The obtained candidate system can be considered as the thought OS. An exact reconstruction of the Rössler system structure was obtained in the paper in such a way. Moreover, in all considered cases, we could not only determine the structure of the OS but also find numerical values for some of the coefficients in the OS.

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Authors and Affiliations

  1. National Technical University of Ukraine “Kyiv Polytechnic Institute”, 37 Prospect Peremogy, Kyiv, 03056, Ukraine

    V. Gorodetskyi & M. Osadchuk

Authors
  1. V. Gorodetskyi
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  2. M. Osadchuk
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Correspondence to V. Gorodetskyi.

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Gorodetskyi, V., Osadchuk, M. Reconstruction of chaotic systems of a certain class. Int. J. Dynam. Control 3, 341–353 (2015). https://doi.org/10.1007/s40435-014-0100-y

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  • DOI: https://doi.org/10.1007/s40435-014-0100-y

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