Numerical Integration

Neural dynamics are systems of differential equations: membrane potentials, gating variables, and ion concentrations all evolve in time according to a right-hand side \(f(t, y)\). braincell turns these equations into runnable simulations through two cooperating pieces:

• a small protocol — DiffEqState and DiffEqModule — that describes what to integrate, and

• a registry of solvers in braincell.quad that decide how to advance the system one step.

The same machinery drives both single-compartment and multi-compartment models, so it lives here as its own topic rather than under either modeling guide. The pages below build up from the mental model to writing your own integrator.

• Overview: How Integration Works
• Defining Differential Equations
• Choosing and Using Solvers
• Advanced Integration

For the exhaustive list of integrators and their signatures, see the API reference.