An interactive tool for visualising two-variable autonomous dynamical systems
- Phase plane: trajectories with directional arrows, vector field, nullclines with tick marks, per-trajectory fixed-point markers, click-to-set initial point
- Kinetic plot: u(t) and v(t) for all visible trajectories, locked to data range
- Stability analysis: fixed points found numerically per trajectory, classified via Jacobian eigenvalues (node, focus, saddle, centre; stable/unstable)
- Theming: Dark / Grey / White themes, per-element colour pickers with opacity
python >= 3.11
PyQt6
pyqtgraph
numpy
scipy
sympy
Install with:
pip install -r requirements.txtpython main.pyDrop a .py file in the models/ directory. It will be auto-discovered at
startup. Required exports:
| Name | Type | Description |
|---|---|---|
META |
dict |
"name" (str), "initial_state" ([u0, v0]), optionally "viewport" (xmin, xmax, ymin, ymax) |
PARAMS |
dict |
Per-parameter dicts with "default", "min", "max", "label" |
model(t, y, params) |
function | Returns [du/dt, dv/dt] |
Optional (auto-generated if absent):
| Name | Description |
|---|---|
guesses(params) |
Starting points for fixed-point search |
isoclines(u_arr, params, **kwargs) |
Returns ((x1,y1), (x2,y2)) for the two nullclines; kwargs may include v_range=(v_min, v_max) from the current viewport |
domain_check(u0, v0) |
Returns (ok: bool, msg: str) — if ok is False the user sees msg as a warning and integration is skipped |
See models/brusselator.py (minimal) and models/fitzhugh_nagumo.py
(no guesses/isoclines - uses auto-generation) for examples.
All colors are stored as #RRGGBBAA (8 hex digits, alpha last), consistent
with CSS/web convention. The alpha channel is exposed in the colour picker.