Repository: Freie Universit├Ąt Berlin, Math Department

Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors

Viennet, Akim and Vercauteren, Nikki and Engel, Maximilian and Faranda, Davide (2022) Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors. Chaos, 32 . pp. 1-15.

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Official URL: https://doi.org/10.1063/5.0093804

Abstract

This study investigates the use of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric sciences applications. In a first step, the needed underlying dynamical models are derived from data using a non-parametric model-based clustering framework. The covariant Lyapunov vectors are then approximated based on these data-driven models. The data-based numerical approach is tested using three well-understood example systems with increasing dynamical complexity, identifying properties that allow for a successful application of the method: in particular, the method is identified to require a clear multiple time scale structure with fast transitions between slow subsystems. The latter slow dynamics should be dynamically characterized by invariant neutral directions of the linear approximation model.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2923
Deposited By: Monika Drueck
Deposited On:06 Apr 2023 07:55
Last Modified:18 Apr 2023 07:56

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