Hamiltonian Lorenz Models

This package implements Hamiltonian Lorenz-like models, a class of low-order dynamical systems that extend the classical Lorenz-96 and Lorenz-2005 frameworks by incorporating a Hamiltonian structure. These models are designed to preserve certain physical invariants—such as energy and Casimirs—making them particularly well-suited for studying conservative dynamical systems, geophysical flows, and chaotic transport.

Installation

Installation within a Python virtual environment:

python3 -m pip install hamlorenz

For more information on creating a Python virtual environment, click here. For a summary with the main steps, click here.

Features

• Hamiltonian structure: The time evolution of the system is derived from a Hamiltonian, preserving energy exactly as in the continuous-time limit.
• Casimir invariants: Multiple conserved quantities beyond energy, ensuring the system evolves on a constrained manifold.
• Symplectic integrators: Optional numerical solvers designed for long-time energy and Casimir invariant preservation.
• Lyapunov spectrum computation: Quantifies the level of chaos in the system via Lyapunov exponents.
• Fourier-based desymmetrization: Enables translational symmetry reduction to study physical variables in a more interpretable form.
• PDF and time series visualization: Built-in tools to analyze and visualize system statistics and dynamics.

Applications

• Modeling barotropic dynamics or simplified atmospheric flows.
• Testing chaos detection and prediction techniques.
• Benchmarking conservative integration schemes.

Reference

For a full mathematical formulation and analysis of these models, see:

Fedele, Chandre, Horvat, and Žagar Hamiltonian Lorenz-like models, Physica D, Vol. 472, 134494 (2025). https://doi.org/10.1016/j.physd.2024.134494

@article{HamLorenz,
  title = {Hamiltonian Lorenz-like models},
  author = {Francesco Fedele and Cristel Chandre and Martin Horvat and Nedjeljka Žagar},
  journal = {Physica D: Nonlinear Phenomena},
  volume = {472},
  pages = {134494},
  year = {2025},
  doi = {https://doi.org/10.1016/j.physd.2024.134494},
}

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Documentation & Examples

Examples can be found at Examples

The full documentation, including detailed function explanations, is available on the Wiki Page.