Forecasting chaotic systems: The role of local Lyapunov exponents

Guégan, Dominique; Leroux, Justin

doi:10.1016/j.chaos.2008.09.017

Cited by 30 publications

(21 citation statements)

References 14 publications

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“…This is repeated a total r times keeping the norms from the Gram-Schmidet (GS). The GS ensures that the direction and rates of growth are measured correctly [11][12][13][14][15]. The Lyapunov exponents are:…”

Section: The Standard Methodsmentioning

confidence: 99%

“…There is dependency between Lyapunov exponents and the chaotic properties of dynamical systems. There are several techniques for finding the Lyapunov exponents of the non-linear systems given by equation 1 [11][12][13][14][15]. However, no single technique appears to be optimal for calculating the Lyapunov exponents.…”

Section: Lyapunov Exponentsmentioning

confidence: 99%

“…A positive LLE indicates that the system is chaotic, while a negative one indicates the non-chaotic behavior. The LLE can also be used to analyze the stability of non-linear systems [15][16][17][18]. A new algorithm was created to satisfy the idea of the suggested methodology; as illustrated in fig.1.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Method for Detecting the Chaotic Behavior in Dynamical Systems With Applications on Chua's System

Mohamed

Darwish

2014

The International Conference on Mathematics and Engineering Phy

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The important step in studying the qualitative behavior of non-linear dynamical system is how to detect the presence of chaos. There are several methods that used to determines the presence of chaos signature. This paper presents a novel method in detecting the presence of chaos. The method combined two techniques namely: the normal form analysis and largest Lyapunov exponent (LLE). Computerized algebraic programs were generated to investigate these two techniques. An example was given to furnish the herein given computer algebra techniques based on real applications. The results obtained in this work were verified with results published by other researchers. The suggested method can provide highly active and efficient ability when studying the nature of non-linear dynamical systems and its chaotic presence.

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Section: The Standard Methodsmentioning

confidence: 99%

Section: Lyapunov Exponentsmentioning

confidence: 99%

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A Novel Method for Detecting the Chaotic Behavior in Dynamical Systems With Applications on Chua's System

Mohamed

Darwish

2014

The International Conference on Mathematics and Engineering Phy

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“…34 Hence, accurate prediction boils down to being able to select the better of the two candidate predictors. Our goal here is to improve on previous work in Guégan & Leroux (2009a, 2009b by developing a systematic selection method to accurately select the best of the two candidates,x…”

Section: Chaoticity Depends On Where You Arementioning

confidence: 99%

“…See, e.g., Gençay (1996), Delecroix et al (1997) and Bask & Gençay (1998). 4 Details on this step of the method can be found in Guégan & Leroux (2009a, 2009b. 5 We followed the z variable of the following Rössler system:…”

Section: Chaoticity Depends On Where You Arementioning

confidence: 99%

Predicting Chaos with Lyapunov Exponents: Zero Plays no Role in Forecasting Chaotic Systems

Guégan

Leroux

2011

Chaotic Systems

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Enhancing water level prediction through model residual correction based on Chaos theory and Kriging

Wang

Babovic

2014

Numerical Methods in Fluids

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SUMMARY Hydrodynamic models based on the physical processes are indispensable tools for predicting water levels in ocean environment. Nonetheless, their accuracies are limited by various factors such as simplifying assumptions, complex ocean bathymetry, and so on. Residual correction, as one of the data assimilation techniques, can extract information from observation and assimilate it into a numerical model to correct the model output directly. Such correction is often performed in two steps: prediction of the model residuals at measured stations followed by spatial distribution at non‐measured locations. For long‐term residual forecast, the accuracy of prediction usually deteriorates with the forecast horizon. In addition to the residual correction at measurement locations, in this paper, we address the critical question as to how to effectively update outputs for computational points without measurements. We develop a hybrid data assimilation procedure, which combines a modified local model (MLM) and an approximated ordinary kriging (AOK). This technique improves the forecasts over a long horizon over the entire computational domain. Using the proposed residual correction technique, the hybrid procedure is examined on a case study of Singapore Regional Model for correcting the water level outputs at locations with and without measurements. In order to provide a comparison, the analysis is carried out throughout prediction horizon of model residuals, tidal residuals, and sea level anomaly, respectively. The comparisons show that the proposed method can successfully assimilate and forecast all variables. Results indicate that resulting prediction accuracy can be significantly improved for all locations of interest independently of the forecast horizon. Copyright © 2014 John Wiley & Sons, Ltd.

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Forecasting chaotic systems: The role of local Lyapunov exponents

Cited by 30 publications

References 14 publications

A Novel Method for Detecting the Chaotic Behavior in Dynamical Systems With Applications on Chua's System

A Novel Method for Detecting the Chaotic Behavior in Dynamical Systems With Applications on Chua's System

Predicting Chaos with Lyapunov Exponents: Zero Plays no Role in Forecasting Chaotic Systems

Enhancing water level prediction through model residual correction based on Chaos theory and Kriging

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