🧠 Dynamic Neuron Model Project

This repository provides multiple numerical and deep learning approaches for solving the Izhikevich neuron model — a well-known system of two ordinary differential equations (ODEs) that simulate spiking neuron behavior efficiently.

📚 About the Izhikevich Model

The Izhikevich model is a biologically plausible spiking neuron model defined by the following two ODEs:

dv/dt = 0.04v² + 5v + 140 - u + I du/dt = a(bv - u)

Where:

• v is the membrane potential of the neuron
• u is a membrane recovery variable
• a, b, c, and d are model parameters
• I is the synaptic input current

This model combines the biological plausibility of Hodgkin-Huxley-type models with the computational efficiency of integrate-and-fire models.

📁 Repository Contents

File / Folder	Description
Explicit_Euler_method/	Solves the Izhikevich model using the Explicit Euler method.
Backward_Euler_method.py	A more stable integration using the Backward Euler method.
Midpoint_(RK2)_method/	Implements the Midpoint (RK2) method.
adaptive_exponential_Rosenbrock/	Advanced stiff solver using exponential Rosenbrock method.
DL_PINN_model/	Uses Physics-Informed Neural Networks (PINNs) to approximate the dynamics of the Izhikevich model.
unity/	(Optional) Unity files for visualization or interaction.

🎯 Goals

• Explore different numerical integration methods for simulating Izhikevich neurons
• Compare solver stability, accuracy, and performance
• Introduce deep learning (PINNs) as an alternative solver
• Offer a clear structure for neuroscience or computational modeling projects

🚀 Getting Started

Requirements

• Python 3.8+
• Required packages: numpy, matplotlib, torch, scipy
• Jupyter Notebook (optional)
• Unity (optional, for interactive visuals)

Example Run

Clone the repo

git clone https://github.com/MohamedBadawy19/Dynamic-Neuron-Model-Project.git cd Dynamic-Neuron-Model-Project

Run a method (example: Explicit Euler)

cd Explicit_Euler_method python simulate_explicit_euler.py

Run the PINN (Physics-Informed Neural Network)

cd DL_PINN_model python train_pinn.py

📊 Output

Each method generates output graphs such as:

Membrane potential v over time

Recovery variable u over time

Raster plots of spiking neuron activity (optional)

These help analyze the model's behavior and compare between solvers.

👨‍💻 Contributors

This is a collaborative educational project developed by Mohamed Badawy and contributors. See the GitHub contributors section for full credit.

📄 License

This project is licensed under the MIT License. You are free to use, modify, and share it with proper attribution.