Phase Plane Widget¶

Interactive phase plane widget for neural mass models, built with anywidget and rendered on HTML5 Canvas.

What It Does¶

This library provides client-side interactive phase plane visualizations for 2D dynamical systems commonly used in computational neuroscience:

Click on the phase plane to set initial conditions and watch the trajectory evolve
Drag parameter sliders to see nullclines, fixed points, and vector fields update in real time
Run parameter sweeps to detect bifurcations — fixed points, limit cycles, and bistability appear automatically
View time series alongside the phase plane

All computation (ODE integration, fixed-point search, nullclines, regime classification) runs in the browser via JavaScript. No Python kernel is needed after the initial load.

Quick Start¶

Jupyter / VS Code¶

pip install phase-plane-widget

from phase_plane_widget import PhasePlaneWidget

widget = PhasePlaneWidget(model_name="mpr")
widget

Static HTML (no kernel)¶

widget.to_standalone_html("widget.html")
# Open widget.html in any browser — works offline

Features¶

Feature	Description
Phase plane	Nullclines, vector field, fixed points, trajectories on HTML5 Canvas
Click-to-set IC	Click anywhere on the phase plane to launch a trajectory
Real-time parameters	Slider controls update the dynamics instantly (no server round-trip)
Time series	Simultaneous plot of state variables vs. time
Bifurcation sweep	Vary one parameter, detect fixed-point / limit-cycle regimes automatically
Regime detection	Auto-classifies: fixed point, limit cycle, or other

Supported Models¶

Model	Variables	Key Parameters	Dynamics
Wilson-Cowan	`E`, `I`	aee, aei, aie, aii, Pe, Pi	E-I population rate model
FitzHugh-Nagumo	`v`, `w`	a, b, ε, I	Excitable neuron
MPR (QIF)	`r`, `v`	Δ, η̄, J, I	Firing-rate + mean voltage (Montbrió, Pazó & Roxin 2015)

Architecture¶

The widget has a dual-mode architecture:

┌─────────────────────────────────────────────────────────────┐
│                     Python (thin wrapper)                    │
│  • Model metadata (param names, defaults, state names)       │
│  • Initial state setup                                       │
│  • to_standalone_html() exporter                             │
└────────────────────────┬────────────────────────────────────┘
                         │  anywidget bridge  (traitlets)
                         │
┌────────────────────────▼────────────────────────────────────┐
│                     JavaScript (full engine)                 │
│  • RK4 ODE solver                                            │
│  • Newton-Raphson fixed-point finder                       │
│  • Nullcline grid-search                                     │
│  • Regime detection (trajectory variance analysis)         │
│  • Parameter sweep engine                                  │
│  • HTML5 Canvas rendering                                    │
└─────────────────────────────────────────────────────────────┘

All heavy computation lives in the browser. The Python layer is a thin wrapper that sets up initial state and provides a programmatic API.

Citation¶

If you use the MPR model, cite:

Montbrió, E., Pazó, D., & Roxin, A. (2015). Macroscopic description for networks of spiking neurons. Physical Review X, 5(2), 021028.