Integration categories

Integration categories#

NEST-compatible models fall into five integration categories that differ in how the underlying ODE (if any) is solved. Knowing a model’s category tells you what numerical method runs under the hood — and, downstream, which validation tolerance applies to it (see Validation status).

Note

These integration categories (how a model is solved) rhyme with the A–E validation tolerance categories (how parity is asserted) but are distinct. A model solved by an adaptive RKF45 integrator (integration category A) is validated under the adaptive-integrator tolerance (validation category A); the analytic iaf_psc family (integration category B) is validated near-exactly (validation category B). They line up by design, but read each in its own page.

Category A — adaptive Runge–Kutta–Fehlberg (RKF45)#

Models with smooth nonlinear sub-threshold dynamics are integrated with an adaptive Runge–Kutta–Fehlberg step (AdaptiveRungeKuttaStep), which adapts the internal step to control local error.

  • Adaptive exponential IAF — aeif_* (e.g. aeif_cond_exp, aeif_psc_alpha).

  • Generalized IF — gif_*.

  • Generalized LIF (Allen Institute) — glif_*.

  • Conductance-based IAF — iaf_cond_* (e.g. iaf_cond_alpha, iaf_cond_exp).

Category B — analytic exact propagators#

Linear current-based IAF neurons have closed-form solutions over a fixed step, so they use exact analytical propagators — no Runge–Kutta iteration is needed. This is the most numerically faithful family (it matches NEST to ~1e-6 mV).

  • Current-based IAF — iaf_psc_* (e.g. iaf_psc_alpha, iaf_psc_exp, iaf_psc_delta).

Category C — Hodgkin–Huxley family (RKF45)#

The Hodgkin–Huxley neurons carry stiff gating dynamics and are also integrated with the adaptive Runge–Kutta–Fehlberg step.

  • Hodgkin–Huxley — hh_psc_*, hh_cond_* (e.g. hh_cond_exp_traub).

  • ht_neuron.

Category D — vectorized rate updates#

Rate-based models have no spike-resolved ODE; their state evolves with a vectorized update pattern applied across the population each step.

  • Linear / nonlinear rate units — lin_rate_*, tanh_rate_*, sigmoid_rate_*, threshold_lin_rate_*.

  • siegert_neuron (mean-field diffusion rate).

Category E — no ODE integration#

Devices and event-driven elements carry no differential equation; they are updated by discrete rules.

  • Devices — generators, recorders, and detectors.

  • Static synapses and gap junctions.

  • Plasticity rules — STP, STDP, and voltage-based learning rules (the weight update is an event-driven kernel, not an integrated ODE; see STDP parity: where state lives and how spikes pair).

See also#