🧮 Population Modeling in MATLAB

This project explores population dynamics using numerical solutions to ordinary differential equations (ODEs). It models real-world biological systems including logistic growth and predator-prey interactions, implemented and visualized entirely in MATLAB.

📈 Features

• Logistic Growth Model: Simulates rabbit population under limited resources using Euler's method.
• Predator-Prey Model: Implements coupled ODEs for rabbit and fox populations using both Euler's method and MATLAB’s ode45 solver.
• Graphical Output: Includes time-based plots, population correlation graphs, and a population animation.
• Video Export: Creates an .avi animation showing dynamic changes in rabbit and fox populations over time.

🧪 Topics Covered

• Euler’s method for solving ODEs
• Logistic growth dynamics
• Lotka-Volterra predator-prey system
• Numerical vs analytical model comparison
• Population modeling and ecological insights

📁 Files

• Project4.m: Main driver script with all logic and plotting functions
• LimitCircle.avi: Video showing the predator-prey population loop (created during runtime)

🚀 How to Run

1. Open MATLAB
2. Ensure Project4.m is in your working directory
3. Run the script by typing:

Project4