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

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  • Bezruchko, Boris P.
  • Smirnov, Dmitry A.
  • Sysoev, Ilya V.

Abstract

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.

Suggested Citation

  • Bezruchko, Boris P. & Smirnov, Dmitry A. & Sysoev, Ilya V., 2006. "Identification of chaotic systems with hidden variables (modified Bock’s algorithm)," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 82-90.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:82-90
    DOI: 10.1016/j.chaos.2005.08.204
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    Cited by:

    1. Bezruchko, B.P. & Ponomarenko, V.I. & Smirnov, D.A. & Sysoev, I.V. & Prokhorov, M.D., 2021. "Class-oriented techniques for reconstruction of dynamics from time series," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Sysoeva, Marina V. & Sysoev, Ilya V. & Prokhorov, Mikhail D. & Ponomarenko, Vladimir I. & Bezruchko, Boris P., 2021. "Reconstruction of coupling structure in network of neuron-like oscillators based on a phase-locked loop," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Ahmadi, Mohamadreza & Mojallali, Hamed, 2012. "Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1108-1120.
    4. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.

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