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Chaos in dynamical systems
Preface 1. Introduction and overview 2. One-dimensional maps 3. Strange attractors and fractal dimensions 4. Dynamical properties of chaotic systems 5. Nonattracting chaotic sets 6. Quasiperiodicity
Controlling chaos
TLDR
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Low dimensional behavior of large systems of globally coupled oscillators.
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear
A Local Ensemble Kalman Filter for Atmospheric Data Assimilation
TLDR
A new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region.
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.
We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from
Stretch, Twist, Fold: The Fast Dynamo
Introduction: the fast dynamo problem fast dynamo action in flows fast dynamo in maps. Methods and their applications: dynamos and non-dynamos magnetic structure in steady integrable flows upper
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