Articles | Volume 26, issue 2
https://doi.org/10.5194/npg-26-73-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-26-73-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 May 2019
Research article |
| 07 May 2019
| 07 May 2019
Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model
Mallory Carlu
CORRESPONDING AUTHOR
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Francesco Ginelli
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
Valerio Lucarini
Department of Mathematics and Statistics, University of Reading, Reading, UK
Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
CEN, University of Hamburg, Hamburg, Germany
Antonio Politi
SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, UK
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Cited
15 citations as recorded by crossref.
- Analysis of a bistable climate toy model with physics-based machine learning methods M. Gelbrecht et al. 10.1140/epjs/s11734-021-00175-0
- Computing Covariant Lyapunov Vectors in Hilbert spaces F. Noethen 10.3934/jcd.2021014
- Online learning of both state and dynamics using ensemble Kalman filters M. Bocquet et al. 10.3934/fods.2020015
- Concept transfer of synaptic diversity from biological to artificial neural networks M. Hofmann et al. 10.1038/s41467-025-60078-9
- Detecting time-irreversibility in multiscale systems: Correlation and response functions in the Lorenz96 model N. Cocciaglia & D. Lucente 10.1063/5.0248658
- Effective models and predictability of chaotic multiscale systems via machine learning F. Borra et al. 10.1103/PhysRevE.102.052203
- Mechanics and thermodynamics of a new minimal model of the atmosphere G. Vissio & V. Lucarini 10.1140/epjp/s13360-020-00814-w
- Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models M. Bocquet et al. 10.5194/npg-26-143-2019
- Learning subgrid-scale models with neural ordinary differential equations S. Kang & E. Constantinescu 10.1016/j.compfluid.2023.105919
- Heterogeneity of the attractor of the Lorenz ’96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties C. Maiocchi et al. 10.1016/j.physd.2023.133970
- Multiscale Postprocessor for Ensemble Streamflow Prediction for Short to Long Ranges B. Alizadeh et al. 10.1175/JHM-D-19-0164.1
- Hamiltonian Lorenz-like models F. Fedele et al. 10.1016/j.physd.2024.134494
- Nested smoothing algorithms for inference and tracking of heterogeneous multi-scale state-space systems S. Pérez-Vieites et al. 10.3934/fods.2025002
- Combining data assimilation and machine learning to infer unresolved scale parametrization J. Brajard et al. 10.1098/rsta.2020.0086
- Using machine-learning modeling to understand macroscopic dynamics in a system of coupled maps F. Borra & M. Baldovin 10.1063/5.0036809
12 citations as recorded by crossref.
- Analysis of a bistable climate toy model with physics-based machine learning methods M. Gelbrecht et al. 10.1140/epjs/s11734-021-00175-0
- Computing Covariant Lyapunov Vectors in Hilbert spaces F. Noethen 10.3934/jcd.2021014
- Online learning of both state and dynamics using ensemble Kalman filters M. Bocquet et al. 10.3934/fods.2020015
- Concept transfer of synaptic diversity from biological to artificial neural networks M. Hofmann et al. 10.1038/s41467-025-60078-9
- Detecting time-irreversibility in multiscale systems: Correlation and response functions in the Lorenz96 model N. Cocciaglia & D. Lucente 10.1063/5.0248658
- Effective models and predictability of chaotic multiscale systems via machine learning F. Borra et al. 10.1103/PhysRevE.102.052203
- Mechanics and thermodynamics of a new minimal model of the atmosphere G. Vissio & V. Lucarini 10.1140/epjp/s13360-020-00814-w
- Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models M. Bocquet et al. 10.5194/npg-26-143-2019
- Learning subgrid-scale models with neural ordinary differential equations S. Kang & E. Constantinescu 10.1016/j.compfluid.2023.105919
- Heterogeneity of the attractor of the Lorenz ’96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties C. Maiocchi et al. 10.1016/j.physd.2023.133970
- Multiscale Postprocessor for Ensemble Streamflow Prediction for Short to Long Ranges B. Alizadeh et al. 10.1175/JHM-D-19-0164.1
- Hamiltonian Lorenz-like models F. Fedele et al. 10.1016/j.physd.2024.134494
3 citations as recorded by crossref.
- Nested smoothing algorithms for inference and tracking of heterogeneous multi-scale state-space systems S. Pérez-Vieites et al. 10.3934/fods.2025002
- Combining data assimilation and machine learning to infer unresolved scale parametrization J. Brajard et al. 10.1098/rsta.2020.0086
- Using machine-learning modeling to understand macroscopic dynamics in a system of coupled maps F. Borra & M. Baldovin 10.1063/5.0036809
Latest update: 15 Oct 2025
Short summary
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.
We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96,...
