Abstract
In this paper surrogate data method of phase-randomized is proposed to identify the random or chaotic nature of the data obtained in dynamic analysis. The calculating results validate the phase-randomized method to be useful as it can increase the extent of accuracy of the results. And the calculating results show that threshold values of the random timeseries and nonlinear chaotic timeseries have marked difference.
Similar content being viewed by others
References
Henry D. I. Abarbanel, Prediction in chaotic nonlinear systems methods for timeseries with broadband Fourier spectra,Phys. B,5 (1991), 1347–1375.
J. Luis Cabrera and F. Javier, Numerical analysis of transient behavior in the discrete random Logistic equation with delay,Phys. Lett. A 197 (1995) 19–24.
Peter Grassberger, Fininte sample corrections to entropy and dimension estimates,Phys. Lett. A,125 (1988), 369–373.
James Theiler, Stephen Eubank, et al., Testing for nonlinearity in time series the method of surrogate data,Physica D,58, (1992), 77–94.
Dean Prichard, The correlation dimension of differenced data,Phys. Lett. A,191 (1994), 245–250.
James Theiler, Spurious dimension from correlation algorithms applied to limited time series data,Phys. Rev. A,34 (1986), 2427–2432.
S. Rombouts, R. Keunen, Investigation of nonlinear structure in multichannel EEG.Phys. Lett. A,202 (1995), 352–358.
Matthew B. Kennel and Strven Isabelle, Method to distinguish possible chaos from colored noise and to determine embedding parameters,Phys. Rev. Lett. A,46 (1992), 3111–3118.
P. E. Rapp and A. M. Albano, Filtered noise can mimic low-dimensional chaotic attractors,Phys. Rev. E,47 (1993), 2289–2297.
Dean Prichard, Generating surrogate data for time series with several simultaneously measured variables,Phys. Rev. Lett.,191 (1994), 230–245.
P. E. Rapp and A. M. Albano, Phase-randomized surrogates can produce spurious identifications of non-random structure,Phys. Lett. A,192 (1994), 27–33.
M. Casdagli and Alistair Mees, Modeling chaotic motions of a string from experimental data,Phys. Rev. E,54 (1992), 303–328.
P. E. Rapp and A. M. Albano, Predicting chaotic time series,Phys. Rev. E,47 (1993), 2289–2297.
Eric J. Kostelich, Problems in estimating dynamics from data,Phys. D,58 (1992), 138–152.
S. J. Schiff and T. Chang, Information transport in temporal systems,Phys. Rev. Lett. A,67 (1992), 378–393.
James Theiler, Some comments on the correlation dimension of noise,Phys. Lett. A,155 (1991), 480–493.
J. Timonen and H. Koskinen, An improved estimator of dimension and some comments on providing confidence intervals,Geophys. Res. Lett.,20 (1993), 1527–1536.
D. Prichard and C. P. Price, Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria.Geophys. Res.,20 (1993), 2817–2825.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Junhai, M., Yushu, C. & Zengrong, L. Threshold value for diagnosis of chaotic nature of the data obtained in nonlinear dynamic analysis. Appl Math Mech 19, 513–520 (1998). https://doi.org/10.1007/BF02453406
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02453406