Reconstructing equations of motion from experimental data with unobserved variables

Breeden, Joseph L.; Hübler, Alfred

doi:10.1103/physreva.42.5817

Cited by 99 publications

(36 citation statements)

References 7 publications

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“…(8) is needed for guaranteeing stability of the overall system and it also controls the rate of synchronization. The condition for convergence of the procedure is that the real parts of the eigenvalues of the Jacobian matrix or the conditional Lyapunov exponents of the overall system are all less than zero [12][13][14][15][16][17] .…”

Section: → W Amentioning

confidence: 99%

Partially blind extraction of continuous chaotic signals from a linear mixture

Liu

et al. 2009

J. Electron.(China)

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In this paper, we address the problem of blind extraction and separation of a continuous chaotic signal from a linear mixture consisting of some chaotic signal and/or random signals. The problem of blind extraction is firstly formulated as a problem of the synchronization-based parameter estimation. Then an efficient least square based parameter estimation method is introduced to determine the desired extracting vector. The proposed blind signal extraction scheme is applicable to blind separation of chaotic signals by formulating the separation problem as the extraction of each chaotic source. Numerical simulation shows that the proposed approach can blindly extract and separate the desired chaotic signals and it is also robust to measurement noise.

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Section: → W Amentioning

confidence: 99%

Partially blind extraction of continuous chaotic signals from a linear mixture

Liu

et al. 2009

J. Electron.(China)

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“…For modeling data by differential equations two approaches can be distinguished depending on whether time derivatives of the process has be estimated from the data or not. Since estimating derivatives form the data amplifies the noise, the former method as applied in [18,11,24,30,31,35] is vulnerable to significant amounts of observational noise as demonstrated in [35].…”

Section: Nonlinear Deterministic Casementioning

confidence: 99%

Determining the Minimum Embedding Dimensions of Input–Output Time Series Data

Cao

Mees

Judd

et al. 1998

Int. J. Bifurcation Chaos

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Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.

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“…al. [2]. Then the distortion matrix is of direct interest in quantifying the uncertainties in the estimates for the hidden variables.…”

Section: Distortionmentioning

confidence: 99%