Estimating covariant Lyapunov vectors from data
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Covariant Lyapunov vectors (CLVs) characterize the directions along which perturbations in dynamical systems grow. They have also been studied as potential predictors of critical transitions and extreme events. For many applications, it is, however, necessary to estimate the vectors from data since model equations are unknown for many interesting phenomena. We propose a novel method for estimating CLVs based on data records without knowing the underlying equations of the system which is suitable also for high-dimensional data and computationally inexpensive. We demonstrate that this purely data-driven approach can accurately estimate CLVs from data records generated by chaotic dynamical systems of dimension 128 and multiple lower-dimensional systems and thus provides the foundation for numerous future applications in data-analysis and data-based predictions.
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