Extensive Chaos in the Lorenz-96 Model
arXiv:0906.3496 · doi:10.1063/1.3496397
Abstract
We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Edward Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and decreases non-monotonically with increasing system size. The length scale describing the deviations from extensivity and the natural chaotic length scale are approximately equal in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. As the forcing is increased at constant system size the fractal dimension exhibits a power-law dependence. The power-law behavior is independent of the system size and quantifies the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.
12 pages, 20 figures
References in corpus (2)
Cited by in corpus (44)
- Neural Granger Causality
- The prediction of future from the past: an old problem from a modern perspective
- Analysing spatially extended high-dimensional dynamics by recurrence plots
- Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
- Revising and Extending the Linear Response Theory for Statistical Mechanical Systems: Evaluating Observables as Predictors and Predictands
- Percolation-based precursors of transitions in extended systems
- A new method for choosing parameters in delay reconstruction-based forecast strategies
- Data-driven closures for stochastic dynamical systems
- Prediction in Projection
- Quantifying Spatiotemporal Chaos in Rayleigh-Bénard Convection
- Feasibility analysis of ensemble sensitivity computation in turbulent flows
- Interpretable Models for Granger Causality Using Self-explaining Neural Networks
- Stability analysis of chaotic systems from data
- A topological perspective on weather regimes
- On the estimation of the Mori-Zwanzig memory integral
- Travelling waves and their bifurcations in the Lorenz-96 model
- The Role of Data in Model Building and Prediction: A Survey Through Examples
- Extraction and Prediction of Coherent Patterns in Incompressible Flows through Space-Time Koopman Analysis
- Standing Swells Surveyed Showing Surprisingly Stable Solutions for the Lorenz '96 Model
- Reconstruction, forecasting, and stability of chaotic dynamics from partial data
- Local dimension and recurrent circulation patterns in long-term climate simulations
- Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model
- Two methods to approximate the Koopman operator with a reservoir computer
- Symmetries in the Lorenz-96 model
- Using Curvature to Select the Time Lag for Delay Reconstruction
- Smoothing and parameter estimation by soft-adherence to governing equations
- An Interpretable and Sparse Neural Network Model for Nonlinear Granger Causality Discovery
- Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere
- Response and flux of information in extended non-equilibrium dynamics
- CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation
- Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers
- Data assimilation empowered neural network parameterizations for subgrid processes in geophysical flows
- Using scaling-region distributions to select embedding parameters
- Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality
- Improving the particle filter in high dimensions using conjugate artificial process noise
- Synchronizing spatio-temporal chaos with imperfect models: a stochastic surface growth picture
- A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations
- Lower bounds on the Lyapunov exponents of stochastic differential equations
- Exploring Spiral Defect Chaos in Generalized Swift-Hohenberg Models with Mean Flow
- Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations
- Chaos in stochastic 2d Galerkin-Navier-Stokes
- Strong Fast Invertibility and Lyapunov Exponents for Linear Systems
- Strategic Monte Carlo Methods for State and Parameter Estimation in High Dimensional Nonlinear Problems
- Stochastically perturbed bred vectors