On a method of estimating chaos control parameters from time series

The algorithm of Ott, Grebogi and Yorke (OGY) is recognized for its efficiency in controlling chaotic dynamical systems, even if the system’s equations are not known and the input data are provided by measured time series in experimental settings. Recently, Santos and Graves (SG) proposed a simple method for estimating the chaos control parameters required by OGY algorithm and applied it to the logistic map. Using only two time series of 100 values, they obtained approximate results for the fixed point case within 2 % of the analytical ones. Although the outputs refer only to a particular case, their conclusion seems to be that the method works as well as in general. To check this statement, we performed a large amount of numerical simulations on different one – dimensional maps. With slight different nuances, our findings were the same so we only presented in the paper the logistic map case. We have noticed that the use of only two short time series implies high risks in a reasonable estimate of the location of the fixed points and of the two control parameters (especially of the second). For large enough number of time series (three or five sets of 400 values each, in the paper) the results provided by numerical simulation approximated the theoretical ones within the limit of a few percent at most. The role played by each method parameter, as the radius for a close encounter of the fixed point or the number of the series and their lengths, is also investigated.

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Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

Discrete Dynamics in Nature and Society ◽

10.1080/10260220290013507 ◽

2002 ◽

Vol 7 (1) ◽

pp. 41-52 ◽

Cited By ~ 7

Author(s):

A. M. López Jiménez ◽

C. Camacho Martínez Vara de Rey ◽

A. R. García Torres

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Chaotic Systems ◽

Chaotic Behavior ◽

Logistic Map ◽

Direct Methods ◽

Short Time Series ◽

Direct Estimation ◽

Non Linear ◽

Short Time

The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation ofλstarting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

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Estimators of Wave Peak Period for Large Return Period Seastates

Volume 6: Ocean Engineering ◽

10.1115/omae2011-50275 ◽

2011 ◽

Author(s):

Michele Drago ◽

Tiziana Ciuffardi ◽

Giancarlo Giovanetti

Keyword(s):

Time Series ◽

Return Period ◽

Barents Sea ◽

Western Mediterranean ◽

Tyrrhenian Sea ◽

Peak Period ◽

Short Time Series ◽

Functional Relationships ◽

Measured Time ◽

Short Time

Different functional relationships for the distribution of the peak period Tp for a given seastate Hs are tested against hindcasted and measured time series for various locations in the European seas, namely Barents Sea, Baltic Sea and Western Mediterranean (Tyrrhenian) Sea. The aim is to investigate their performance when extrapolating from available data for the estimation of the long return period seastates which are not covered by the length of the time series. A second complementary objective of the paper is to quantify the uncertainty and the variability that can occur in the estimation of the Hs/Tp association when a short time series is available. This is done by assessing the Hs/Tp relation from a 35-years long time series that will be considered as the correct one. Then it will be compared with those obtained by analysing multiple cases of shorter and shorter portions of the time series. The spread of the results against the one obtained with the entire time series will be estimated to give some indications about how long a time series has to be to ensure a correct extrapolation to the long return period seastates and to provide an indication of the error that can affect the results when a short time series is available.

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A strategy for meta-analysis of short time series microarray datasets

Frontiers in Bioscience ◽

10.2741/3512 ◽

2009 ◽

Vol Volume (14) ◽

pp. 4058 ◽

Cited By ~ 2

Author(s):

Ruping Sun

Keyword(s):

Time Series ◽

Meta Analysis ◽

Short Time Series ◽

Microarray Datasets ◽

Short Time ◽

Time Series Microarray

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Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study

Journal of NeuroEngineering and Rehabilitation ◽

10.1186/s12984-021-00872-w ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Tie Liang ◽

Qingyu Zhang ◽

Xiaoguang Liu ◽

Bin Dong ◽

Xiuling Liu ◽

...

Keyword(s):

Time Series ◽

Information Flow ◽

Gamma Band ◽

Motor Dysfunction ◽

Beta Band ◽

Short Time Series ◽

Information Interaction ◽

Stroke Group ◽

Short Time ◽

Maximal Information Coefficient

Abstract Background The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients. Methods We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients. Results The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group. Conclusions The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

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Improved Lempel-Ziv Algorithm Based on Complexity Measurement of Short Time Series

Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007) ◽

10.1109/fskd.2007.357 ◽

2007 ◽

Cited By ~ 4

Author(s):

Feng-tao Liu ◽

Yong Tang

Keyword(s):

Time Series ◽

Short Time Series ◽

Complexity Measurement ◽

Short Time

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A reliable measure of similarity based on dependency for short time series: an application to gene expression networks

BMC Bioinformatics ◽

10.1186/1471-2105-10-270 ◽

2009 ◽

Vol 10 (1) ◽

pp. 270 ◽

Cited By ~ 1

Author(s):

Mônica G Campiteli ◽

Frederico M Soriani ◽

Iran Malavazi ◽

Osame Kinouchi ◽

Carlos AB Pereira ◽

...

Keyword(s):

Gene Expression ◽

Time Series ◽

Reliable Measure ◽

Short Time Series ◽

Measure Of Similarity ◽

Short Time

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LIMITATIONS OF THE PANEL REGRESSION MODEL APPLICATION: THE EXAMPLE OF THE WESTERN BALKAN COUNTRIES

ACTA ECONOMICA ◽

10.7251/ace2032151b ◽

2021 ◽

Vol 18 (32) ◽

Author(s):

Stanko Stanić ◽

Bojan Baškot

Keyword(s):

Time Series ◽

Regression Model ◽

Time Frame ◽

Panel Regression ◽

Time Dimension ◽

Data Set ◽

Short Time Series ◽

Western Balkan Region ◽

Balkan Region ◽

Short Time

Panel regression model may seem like an appealing solution in conditions of limited time series. This is often used as a shortcut to achieve deeper data set by setting several individual cases on the same time dimension, where cross units visually but not really multiply a time frame. Macroeconometrics of the Western Balkan region assumes short time series issue. Additionally, the structural brakes are numerous. Panel regression may seem like a solution, but there are some limitations that should be considered.

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