Two-Dimensional Phase Portrait Plotter

Hi! I made a two-dimensional phase portrait plotter website page.

Purpose: If you don't have any study guide for exercises related to dynamic systems or too lazy to run python and set up sliders to visually see potential bifurcations, you can play around with said dynamic system (numerically) to visually get a feel of the system.

It includes numerical approximations for:

- Euler/4th Order Runge-Kutta solver for the system --> You can also pick initial point + backwards integration.

- Poincaré Index (index theory)

- Nullclines

- Eigenvalues of the Jacobian matrix (sometimes called "stability matrix" in the literature)

It's based on old python code that I made for a dynamic system course that I converted to JavaScript using Grok, Sonnet 4.5 and Gemini Pro.

Does not include:

- Bifurcation diagrams - can't make it without a computer algebra system (CAS), way above my skill level...

- Anything that isn't two-dimensional (for one dimension you can just use a regular calculator) - 3D got highly computational heavy fast (for a website so to speak). I'm keeping it simple since it is a practice tool to draw your own phase portraits yourself by hand (like most exams requires you to do).

For real applications, you need to either solve stuff analytically or use more advance tools. This is just for educational purposes and enjoyment.