Lorenz63 🌀

📌 Overview

The Lorenz system is a simplified model for atmospheric convection introduced by Edward Lorenz in 1963. It consists of three ODEs:

$$\frac{dx}{dt} = \sigma(y − x)$$ $$\frac{dy}{dt} = x(\rho − z) − y$$ $$\frac{dz}{dt} = xy − \beta z$$

This project explores numerical solutions and the chaotic behavior of the Lorenz attractor.

🚀 Features

• RK4 integration of the Lorenz system
• 2D/3D trajectory plots
• Sensitivity to initial conditions
• Least squares analysis of divergence

📁 Project Structure

Lorenz63/
├── 01_report/ # PDF and LaTeX report (documentation and analysis)
├── 02_src/ # Source code (Jupyter notebooks, Python scripts)
├── LICENSE # MIT License
└── README.md # Project documentation

🛠 Dependencies

This project uses the following Python libraries:

• numpy — numerical computing and array operations
• scipy — solving ODEs and cubic spline interpolation
• matplotlib — 2D and 3D plotting
• plotly — interactive 3D visualizations
• pandas — organizing and exporting data tables
• tabulate — rendering tables in notebook-friendly formats
• scikit-learn — performance metrics (MAE, MSE, explained variance)

👥 Authors

• Julio Cezar de Moura Lima
• Lucas Amaral Taylor