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• W1625989812 abstract "The theme of this thesis is the synchronization of coupled chaotic systems.Background and introductory material are presented in Chapter 1.In Chapter 2,we study the transition to coherence of ensembles of globallycoupled chaotic maps allowing for ensembles of non-identical maps andfor noise. The transition coupling strengthis determined from a transfer function of the perturbation evolution.Analytical results are presented and tested using numericalexperiments.One of our examples suggests that the validity of the perturbationtheory approach can be problematic for an ensemble of noiselessidentical `nonhyperbolic' maps, but can be restored by noise and/or parameter spread.The problem of estimating the state of a largeevolving spatiotemporally chaotic system from noisy observationsand a model of the system dynamicsis studied in Chapters 3 - 5.This problem, refered to as `data assimilation', canbe thought of as a synchorization problemwhere one attempts to synchronize the model state to the systemstate by using incoming data to correctsynchronization error.In Chapter 3, using a simple data assimilation technique, we show the possibleoccurrence of temporally and spatially localized burstsin the estimation error. We discuss the similarity of these burststo those occurring at the `bubbling transition' inthe synchronization of low dimensional chaotic systems.In general, the model used for state estimationis imperfect and does not exactly represent the system dynamics.In Chapter 4 we modify an ensemble Kalman filter schemeto incorporate the effect of model biasfor large chaotic systems based on augmentation of the systemstate by the bias estimates,and we consider different ways of parameterizingthe model bias.The experimental results highlight the critical role played by the selectionof a good parameterization model for representing the form ofthe possible bias in the model.In Chapter 5 we further test the method developed inChapter 4 via numerical experiments employing previouslydeveloped codes for global weather forecasting. The results suggestthat our method can be effective for obtaining improved forecastingresults when using an ensemble Kalman filter scheme." @default.
• W1625989812 created "2016-06-24" @default.
• W1625989812 creator A5013993810 @default.
• W1625989812 date "2007-11-27" @default.
• W1625989812 modified "2023-09-23" @default.
• W1625989812 title "Synchronization in chaotic systems: Coupling of chaotic maps, data assimilation and weather forecasting" @default.
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• W1625989812 hasPublicationYear "2007" @default.
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