LYAPUNOV-EXPONENT SPECTRUM FROM NOISY TIME SERIES

2013 ◽  
Vol 23 (06) ◽  
pp. 1350103 ◽  
Author(s):  
TIAN-LIANG YAO ◽  
HAI-FENG LIU ◽  
JIAN-LIANG XU ◽  
WEI-FENG LI
Keyword(s):  
Time Series ◽  
Lyapunov Spectrum ◽  
Deterministic System ◽  
Hénon Map ◽  
Henon Map ◽  
Noisy Time Series ◽  
Generalized Hénon Map ◽  
Novel Method ◽  
Influence Of Noise ◽  
Lyapunov Exponent Spectrum

Since all kinds of noise exist in signals from real-world systems, it is very difficult to exactly estimate Lyapunov exponents from this time series. In this paper, a novel method for estimating the Lyapunov spectrum from a noisy chaotic time series is presented. We consider the higher-order mappings from neighbors into neighbors, rather than the mappings from small displacements into small displacements as usual. The influence of noise on the second-order mappings is researched, and an averaging method is proposed to cope with this noise. The mappings equations of the underlying deterministic system can be obtained from the noisy data via the method, and then the Lyapunov spectrum can be estimated. We demonstrate the performance of our algorithm for three familiar chaotic systems, Hénon map, the generalized Hénon map and Lorenz system. It is found that the proposed method provides a reasonable estimate of Lyapunov spectrum for these three systems when the noise level is less than 20%, 10% and 7%, respectively. Furthermore, our method is not sensitive to the distribution types of the noise, and the results of our method become more accurate with the increase of the length of time series.

scholarly journals Time series classification based on triadic time series motifs

2019 ◽  
Vol 33 (21) ◽  
pp. 1950237
Author(s):  
Wen-Jie Xie ◽  
Rui-Qi Han ◽  
Wei-Xing Zhou
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Time Series Classification ◽  
Similarity Coefficients ◽  
Motif Analysis ◽  
Hénon Map ◽  
Henon Map ◽  
Motif Occurrence ◽  
Generalized Hénon Map ◽  
Dynamic Time

It is of great significance to identify the characteristics of time series to quantify their similarity and classify different classes of time series. We define six types of triadic time-series motifs and investigate the motif occurrence profiles extracted from the time series. Based on triadic time series motif profiles, we further propose to estimate the similarity coefficients between different time series and classify these time series with high accuracy. We validate the method with time series generated from nonlinear dynamic systems (logistic map, chaotic logistic map, chaotic Henon map, chaotic Ikeda map, hyperchaotic generalized Henon map and hyperchaotic folded-tower map) and retrieved from the UCR Time Series Classification Archive. Our analysis shows that the proposed triadic time series motif analysis performs better than the classic dynamic time wrapping method in classifying time series for certain datasets investigated in this work.

scholarly journals Tracking bifurcation curves in the Hénon map from only time-series datasets

2019 ◽  
Vol 10 (2) ◽  
pp. 268-278
Author(s):  
Yoshitaka Itoh ◽  
Masaharu Adachi
Keyword(s):  
Time Series ◽  
Hénon Map ◽  
Henon Map

Hash function based on the generalized Henon map

2008 ◽  
Vol 17 (5) ◽  
pp. 1685-1690 ◽  
Author(s):  
Zheng Fan ◽  
Tian Xiao-Jian ◽  
Li Xue-Yan ◽  
Wu Bin
Keyword(s):  
Hash Function ◽  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map

Transient chaos in a generalized Hénon map on the torus

1988 ◽  
Vol 126 (7) ◽  
pp. 405-410 ◽  
Author(s):  
F.M. Izrailev ◽  
B. Timmermann ◽  
W. Timmermann
Keyword(s):  
Transient Chaos ◽  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map

scholarly journals Generalized Hénon Map and Bifurcations of Homoclinic Tangencies

2005 ◽  
Vol 4 (2) ◽  
pp. 407-436 ◽  
Author(s):  
V. S. Gonchenko ◽  
Yu. A. Kuznetsov ◽  
H. G. E. Meijer
Keyword(s):  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map ◽  
Homoclinic Tangencies

scholarly journals Hopf Bifurcation of the Higher Dimensional Hénon Map

2019 ◽  
Vol 67 (1) ◽  
pp. 73-78
Author(s):  
Saiful Islam ◽  
Chandra Nath Podder
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Explicit Criterion ◽  
Hénon Map ◽  
Henon Map ◽  
Higher Dimensional ◽  
Generalized Hénon Map

In this paper, the discrete time generalized Hénon map is considered and the existence of Hopf bifurcation via an explicit criterion for N≥3, in particular for N=4 and N=5 has given. The relation between the parameters a and b as well as the range of the values of the parameters for N=3,4,5 has driven and the existence of Hopf bifurcation is demonstrated for the values of the parameters calculated from their relations. The results of numerical simulations for different values of the parameters are also presented. Dhaka Univ. J. Sci. 67(1): 73-78, 2019 (January)

GLOBAL DYNAMICAL EQUATIONS AND LYAPUNOV EXPONENTS FROM NOISY CHAOTIC TIME SERIES

1993 ◽  
Vol 03 (03) ◽  
pp. 607-616 ◽  
Author(s):  
JAMES B. KADTKE ◽  
JEFFREY BRUSH ◽  
JOACHIM HOLZFUSS
Keyword(s):  
Time Series ◽  
Original System ◽  
Lyapunov Spectrum ◽  
Model Quality ◽  
Dynamical Equations ◽  
Numerical Noise ◽  
Noisy Time Series ◽  
Reconstructed Phase Space ◽  
Dynamical Invariants

We discuss the extraction of few-parameter, global dynamical models from noisy time series of chaotic systems. In particular, we consider the class of models which are approximations to sets of dynamical equations in the reconstructed phase space. We show that certain numerical methods significantly improve the quality of the resulting models, and central to these methods is the idea of eliminating model terms which are “dynamically insignificant” and add only numerical noise. For the purposes of the paper, we quantify model quality by the rather strict measure of its ability to recover the dynamical invariants of the original system, in particular, the Lyapunov spectrum. Consequently, we also postulate that by first extracting a global model, the Lyapunov spectrum of a generating system can be recovered from time series whose noise levels are much higher than current algorithms would allow. We present several numerical examples to demonstrate the above ideas.

New enciphering algorithm based on chaotic generalized Hénon map

Chaos Theory ◽  
2011 ◽  
Author(s):  
Octaviana Datcu ◽  
Jean-Pierre Barbot ◽  
Adriana Vlad
Keyword(s):  
Hénon Map ◽  
Henon Map ◽  
Generalized Hénon Map
Sign in / Sign up

Export Citation Format

Share Document