Abstract
The largest Lyapunov exponent is an essential criterion to judge whether the time series are chaos or not. But traditional methods have some disadvantages such as calculated amount is large and calculated time is long, which lead to these methods have limitations in engineering application. An improved algorithm based on space grid method for estimating the largest Lyapunov exponent is presented in this paper. The whole reconstructed phase space is divided into many small spaces in the algorithm. Only the points locating in the subspace are the reference point exist are searched when needed, and thus the fast searching speed is gained. Simulation results show that neighborhoods can be searched quickly by the suggested algorithm. At the same time, the algorithm is robust and easy to be programmed.
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References
Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica 16D, 285–317 (1985)
Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134 (1993)
Friedman, J.H., Bentley, J.L., Finkel, R.A.: ACM Trans. Math. Soft. 3, 209 (1977)
Oiwa, N.N., Fiedler-Ferrara, N.: A fast algorithm for estimating Lyapunov exponents from time series. Physics Letters A 246, 117–121 (1998)
Xiong, B., He, M., Yu, H.: Algorithm for Finding k-Nearest Neighbors of Scattered Points in Three Dimension. Journal of Computer-aided Design & Computer Graphcis 16(7), 909–917 (2004)
Kim, H.S., Eykholt, R., Salas, J.D.: Nonlinear dynamics, delay times, and embedding windows. Physica D 127, 48–60 (1999)
Yang, S., Zhang, X., Zhao, C.: A steady algorithm to estimating the largest Lyapunov exponent. Acta Physica Sinica 49(4), 636–640 (2000)
Liu, S., Zhu, S., Yu, X.: Study on Phase Space Reconstruction Optimization. Journal of Data Acquisition & Processing 23(1), 65–69 (2008)
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© 2012 Springer-Verlag Berlin Heidelberg
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Yang, A., Wang, J., Liu, S., Wei, X., Yang, Q. (2012). An Improved Algorithm for Estimating the Largest Lyapunov Exponent. In: Zhao, M., Sha, J. (eds) Communications and Information Processing. Communications in Computer and Information Science, vol 288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31965-5_5
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DOI: https://doi.org/10.1007/978-3-642-31965-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31964-8
Online ISBN: 978-3-642-31965-5
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