ChaosSyncPy

A modular Python framework for chaotic/hyperchaotic synchronization, nonlinear control, disturbance analysis, and dynamical systems research.

Overview

ChaosSyncPy is a flexible and extensible framework for the simulation and synchronization of nonlinear and chaotic/hyṕerchaotic dynamical systems.

A key feature of the framework is its dimension-agnostic design, allowing the implementation of dynamical systems with an arbitrary number of state variables. This makes it suitable not only for classical low-dimensional chaotic systems (such as the Lorenz system), but also for higher-dimensional or augmented systems, including those with additional control states, observers, or learning-based components.

The project provides a modular architecture for implementing master-slave synchronization schemes, control laws, disturbances, and numerical integration methods.

The framework is intended for researchers, students, and engineers working in areas such as:

• Chaotic systems
• Nonlinear control
• Synchronization
• Dynamical systems
• System identification

---

Features

• Modular architecture
• Master-slave synchronization framework
• Configurable numerical solvers (RK45, BDF, Radau, etc.)
• Configurable disturbances
• Error convergence analysis
• Attractor visualization
• Easily extensible to new dynamical systems and controllers

---

Installation

Clone the repository:

git clone https://github.com/felipeofugi/ChaosSyncPy.git
cd ChaosSyncPy

Create and activate a virtual environment:

python3 -m venv .venv
source .venv/bin/activate

Install the required packages:

pip install -r requirements.txt

---

Running a Simulation

Define the state names and the plant of the dynamic system to be simulated in:

src/system.py

Enter the initial conditions of the master and slave systems and the type of disturbance in:

main.py

Edit the disturbances in:

src/disturbances.py

Set the control signal in:

src/controller.py

Execute:

python main.py

The graphs will be generated in the figures directory.

Simulation parameters can be configured in:

src/config.py

The generated graphs can be edited in

src/plots.py

---

Implemented Systems (Example)

Lorenz System

The Lorenz system is one of the most studied chaotic systems and is defined by:

$$ \dot{x} = \sigma (y - x) $$

$$ \dot{y} = x(\rho - z) - y $$

$$ \dot{z} = xy - \beta z $$

where:

• $\sigma = 10$
• $\rho = 28$
• $\beta = 8/3$

---

Master-Slave Synchronization

The framework supports synchronization between a master and a slave Lorenz system through a configurable control law.

States

---

Synchronization Error

---

Attractors

---

Project Structure

ChaosSyncPy/
│
├── figures/
├── src/
│   ├── config.py
│   ├── controller.py
│   ├── disturbances.py
│   ├── integrator.py
│   ├── plots.py
│   ├── synchronization.py
│   ├── system.py
│   └── __init__.py
│
├── main.py
├── requirements.txt
├── LICENSE
└── README.md

---

License

This project is distributed under the MIT License.

---

Citation

If you use this project in academic research, please consider citing the repository in your publications.