Izhikevich Neuron Model Simulation

This repository contains a Python implementation of the Izhikevich neuron model to simulate Regular Spiking (RS) neurons.

Table of Contents

• Introduction
• Requirements
• Code Structure
• How the Code Works
• Running the Notebook
• Example Plots
• References

Introduction

The Izhikevich neuron model is a mathematical representation of cortical spiking neurons. This simulation studies the RS neuron's response to varying external input levels.

Requirements

• Python 3.x
• NumPy
• Matplotlib
• Jupyter Notebook

Code Structure

• Problem2.ipynb: Interactive Jupyter Notebook for simulation and plotting

How the Code Works

Imports

The code starts by importing necessary libraries:

• numpy for numerical computations
• matplotlib.pyplot for plotting

Izhikevich Model Implementation

The Izhikevich model is implemented using two coupled differential equations:

• Equation (1): dv/dt = 0.04v^2 + 5v + 140 - u + I(t)
• Equation (2): du/dt = a(bv - u)

with the condition:

• if v >= 30, v = c, u = u + d

Simulation Parameters

The simulation parameters are:

• a, b, c, d: Izhikevich model parameters
• I_values: array of external input levels
• steps: number of simulation steps
• tau: time step

Simulation Loop

The simulation loop iterates over:

• External input levels (I_values)
• Time steps (steps)

Plotting

The code generates two plots:

• Membrane potential time-series for varying input levels
• Mean spike rate vs. input level plot

Running the Notebook

1. Clone the repository: git clone https://github.com/fardeen0424/Izhikevich-Neuron-Model-Simulation
2. Install required libraries: pip install numpy matplotlib
3. Run Jupyter Notebook: jupyter notebook Problem2.ipynb
4. Run Jupyter Notebook: jupyter notebook Problem3.ipynb
5. Follow instructions in the notebook to simulate and plot RS neuron behavior

Example Plots

• Membrane potential time-series for varying input levels

• 

• Mean spike rate vs. input level plot

References

• Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6), 1569-1572.
• Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks, 15(5), 1063-1070.