Why not use Hodgkin–Huxley for every cell?

HH is expensive and focuses on channel kinetics of one spike. LIF keeps only leak, threshold, reset, and synapses, so a small network and a raster stay interactive in the browser.

What does the synchrony readout mean?

Values near 1 mean many neurons fire in tight volleys; values near 0 mean asynchronous irregular firing. Coupling, shared drive, and noise trade off those regimes.

What does the refractory period do?

After a spike the voltage is clamped at reset for τref, imposing a hard maximum rate ~1/τref and preventing immediate re-fire from leftover synaptic current.

Integrate-and-Fire Neuron Network

Leaky LIF neurons with refractory period, synaptic weights, raster plot, membrane traces, and a synchrony readout.

Simulation

Presets

AI: subthreshold drive, noise, sparse graph. Volleys: strong excitatory all-to-all. Weak: ring, small w. Inhibition: negative w with a large shared I_ext.

LIF parameters

Neurons N24

I_ext (R = 1)19.5

τm20 ms

τref2 ms

τs3.5 ms

Vth-50 mV

noise σ9

coupling w10

Connectivity

Each cell is leaky integrate-and-fire (leak, threshold, reset, refractory) — not Hodgkin–Huxley gates and not FitzHugh–Nagumo. A spike of j jumps I_syn,i by w W_ij; I_syn then decays with τs. W is 1/(N−1) all-to-all, 1/degree on a ring, or Erdős–Rényi (p = 0.2) scaled to the same mean incoming weight. Negative w is inhibition. Changing N rebuilds the arrays on reset.

Shortcuts

Space / Enter — play / pause
P — pause / resume
R — reset network

Measured values

pop. rate0.0Hz

synchrony0.000

spikes in window0

τref max rate500Hz

t0ms

N24

This page is leaky integrate-and-fire, not a Hodgkin–Huxley axon and not the FitzHugh–Nagumo “HH network”. Spikes are threshold events; the action-potential waveform is omitted on purpose so a raster of N cells stays interactive.

About this model

Each neuron is a leaky integrate-and-fire unit: τm V′=−(V−Vrest)+R Iext+R Isyn, with a spike when V reaches Vth, reset to Vreset, and a refractory interval τref. Synapses are current-based: a presynaptic spike adds a jump or exponential pulse weighted by wij. The canvas shows a raster of spike times, a few membrane traces, and a population synchrony score (e.g. pairwise coincidence or Kuramoto order on recent spikes). This is not Hodgkin–Huxley or FitzHugh–Nagumo — those pages model the action-potential waveform.

Who it's for: Computational neuroscience and neural-engineering introductions to spiking networks.

Key terms

Leaky integrate-and-fire
Refractory period
Raster plot
Synaptic weight
Synchrony
Threshold

How it works

A network of leaky integrate-and-fire neurons: each cell leaks toward rest, spikes at threshold, resets, and is silent for a refractory interval. Current-based synapses jump on every presynaptic spike and decay exponentially. The canvas is a scrolling spike raster plus three membrane traces and a population synchrony score.

Key equations

τ_m V̇_i = −(V_i − V_rest) + R (I_ext + I_syn,i + I_noise,i), V_i ≥ V_th and not refractory → spike, V_i ← V_reset, refractory timer = τ_ref. τ_s İ_syn = −I_syn; on a spike of j, for each i: I_syn,i ← I_syn,i + w W_ij. Synchrony (0–1) blends mean pairwise spike coincidence in an 80 ms window (±4 ms) with a Kuramoto order from last-ISI phases φ_i = 2π (t − t_i)/ISI_i. R = 1, V_rest = −70 mV, V_reset = −78 mV. Forward Euler, dt = 0.05 ms. I_noise is an OU current (Box–Muller) plus a quenched bias.

Frequently asked questions

Why not use Hodgkin–Huxley for every cell?: HH is expensive and focuses on channel kinetics of one spike. LIF keeps only leak, threshold, reset, and synapses, so a small network and a raster stay interactive in the browser.
What does the synchrony readout mean?: Values near 1 mean many neurons fire in tight volleys; values near 0 mean asynchronous irregular firing. Coupling, shared drive, and noise trade off those regimes.
What does the refractory period do?: After a spike the voltage is clamped at reset for τref, imposing a hard maximum rate ~1/τref and preventing immediate re-fire from leftover synaptic current.

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