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

Akim Viennet (1) , Nikki Vercauteren (2) , Maximilian Engel (3) , Davide Faranda (4, 5, 6, 7)

1 FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris
2 Department of Geosciences [Oslo]
3 Department of Mathematics and Computer Science
4 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)
5 London Mathematical Laboratory
6 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
7 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation

We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The underlying models are built from data by the dynamical clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated based on these models. We test this data-based numerical approach at the hand of three well-understood example systems with increasing dynamical complexity, identifying crucial properties that allow for a successful application of the method: in particular, it turns out that the method requires a clear multiple time scale structure with fast transitions between slow subsystems which can be dynamically characterized by invariant neutral directions of the linear approximation model.

Domaines: Dynamique Chaotique [nlin.CD]; Systèmes dynamiques [math.DS]

Akim Viennet, Nikki Vercauteren, Maximilian Engel, Davide Faranda. Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors. 2022. ⟨hal-03626146v1⟩