Simulations

Interactive simulations and games for exploring mathematical models and practicing qualitative reasoning. Each runs directly in your browser, with no installation required.

Dynamical systems and excitable cells

• Morris–Lecar simulator: Explore membrane voltage, phase planes, excitability, oscillations, and saddle manifolds in a reduced conductance-based model.
• Slow passage through Hopf: Compare supercritical and subcritical Hopf normal forms under parameter ramps, including delay, memory, and noise.

Biophysics and qualitative reasoning

• Current–voltage relation game: Practice interpreting reversal potentials, activation, conductance, and slope from current–voltage curves.
• Voltage-clamp game: Infer reversal potentials from voltage-clamp current traces, then reveal the underlying relationships.
• PolyQual game: Compare polynomial curves using the signs of the function and its first two derivatives.

Probability and perception

• Retaliation simulation: Explore stochastic event frequency and size, then compare expected and observed activity. This stylized perception game is a toy model, not a validated model of conflict escalation.

The simulations retain their scientific references and source repository identifiers and exact source commits. Existing standalone app links remain available. Source commits and provenance.