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Interactive Demos

Each demo below is a live, self-contained widget running entirely in your browser. No Python kernel, no server — just HTML5 Canvas + JavaScript.

Click on the phase plane to set initial conditions, drag sliders to change parameters, and run parameter sweeps to explore bifurcations.

Wilson-Cowan: E-I Oscillations

A classic excitatory-inhibitory population model. Default parameters produce stable fixed points; increase aee (E→E coupling) or Pe (external drive) to induce oscillations.

FitzHugh-Nagumo: Excitability

Simplified Hodgkin-Huxley dynamics. Below the bifurcation threshold (I ≈ 0.3) the neuron rests at a stable fixed point. Above threshold, it fires repetitively (limit cycle).

MPR: Bistable Regime

The Montbrió-Pazó-Roxin model in its bistable regime: three coexisting fixed points (stable low-activity node, saddle, stable high-activity focus). Click near the saddle to observe the separatrix — trajectories diverge to either the low or high activity state.

MPR: Limit Cycle

Just beyond the bistable region, the MPR model exhibits limit cycle oscillations in firing rate. This corresponds to a Hopf bifurcation from the high-activity fixed point.

Hindmarsh–Rose: 3D Bursting Neuron

A three-variable phenomenological model of neuronal bursting. The fast subsystem (x, y) generates action potentials while the slow adaptation current z modulates the burst period. With the default parameters (a=1, b=3, c=1, d=5, I=3, r=0.001, s=4, x_r=-1.6) the model produces rich square-wave bursting — trains of spikes followed by silent quiescent phases. Decrease b to cross the transition to plateau-like bursting, or increase I to enter tonic spiking.

Custom Model Editor

This demo pre-loads the MPR (QIF) equations into the live editor so you can tweak them interactively. Try adding extra terms (e.g. -r^3 for firing-rate adaptation) or changing the noise strength.

The editor is open by default — edit the equations and the plots update automatically (debounced 500 ms).

How These Work

Each iframe loads a standalone HTML export generated by PhasePlaneWidget.to_standalone_html(). The file contains:

  • All model equations in JavaScript
  • An RK4 ODE solver
  • A Newton-Raphson fixed-point finder
  • Canvas rendering code
  • No external dependencies — works offline

To generate your own:

from tvb_phaseplane import PhasePlaneWidget

widget = PhasePlaneWidget(model_name="mpr")
widget.params["eta_bar"] = -5.0
widget.params["J"] = 15.0
widget.to_standalone_html("my_widget.html")