🧠 Spiking Neural Network — LIF & STDP

A network of 50 Leaky Integrate-and-Fire (LIF) neurons (40 excitatory, 10 inhibitory) with spike-timing-dependent plasticity (STDP). Each neuron follows τ_m·dV/dt = −(V − V_rest) + R_m·I. Watch synchronous bursting in the raster plot and voltage trace below.

Raster plot — each dot is a spike (excitatory = purple, inhibitory = red)

Membrane voltage — neuron #0 (V_thresh = −55 mV, dashed)

Drive

Input current I_ext 1.5 µA Noise σ 0.5

Connectivity

Coupling g 1.0 E/I ratio 4:1

Plasticity

STDP A₊ (LTP) 0.01 A₋ (LTD) 0.012

Statistics

Firing rate—

Synchrony—

Burst period—

Spikes / s—

LIF Model & STDP

Each neuron integrates synaptic and external input: τ_m·dV/dt = −(V − V_rest) + R_m·I_total. When V exceeds the threshold V_thresh = −55 mV a spike is emitted, V resets to −75 mV, and a 2 ms absolute refractory period begins. Synaptic currents decay exponentially with τ_syn = 3 ms. STDP adjusts weights based on the time difference between pre- and post-synaptic spikes: Δw = A₊·exp(−|Δt|/τ₊) for causal pairs (potentiation) and Δw = −A₋·exp(−|Δt|/τ₋) for anti-causal pairs (depression).