Spiking neuron model Sample Clauses

Spiking neuron model. Hybrid models describe the continuous evolution of several state variables (including a “membrane voltage” and auxiliary “currents”) and discrete events associated to the spiking event, i.e. special rules applied to (a subset of) the state variables. Well known are the Xxxxxxx-Xxxxxx (HH) (Xxxxxx, 1952), the leaky integrate-and-fire (LIF) and the Izhikevich (IZH) (Xxxxxxxxxx, 2003). For this experiment we adopted the IZH model which is computationally efficient (13 – 26 operations per simulated ms per neuron), and yet capable of replicating the spiking behaviour of several neuron types (Xxxxxxxxxx, 2004). ⎛ ∆𝒗 = 𝒗(𝒕)𝟐 − 𝒖(𝒕) + 𝑰(𝒕) ⎪𝒊𝒇 𝒗(𝒕) < 𝑣𝑝𝑒𝑎𝑘 𝑡ℎ𝑒𝑛 {∆𝒕 ⎪ = 𝒂(𝒃𝒗(𝒕) − 𝒄) ⎨ 𝒗(𝒕) = 𝑣𝑝𝑒𝑎𝑘 ⎪ ⎪𝒊𝒇 𝒗(𝒕) ≥ 𝑣𝑝𝑒𝑎𝑘 𝑡ℎ𝑒𝑛 {𝒗(𝒕 + ∆𝒕) ← 𝒄 where: 𝒖(𝒕 + ∆𝒕) ← 𝒖(𝒕) + 𝒅 • v (t) is the neural membrane potential. This is the key observable; we say that when v reaches vpeak a “neural spike” happened; • I(t) is the potential change generated by the sum of all synapses incoming to the neuron. Incoming currents are present if spikes arrived form presynaptic neurons; • u(t) is an auxiliary variable (the recovery current bringing back v to equilibrium); • a, b, c, d are four parameters, constant for each neuron kind, by varying them the same equation models several kind of known neural types. In this experiment we used a mix of 80% excitatory RS Izhikevich neurons (i.e.: a=0.02, b=0.2, c = -65.0 mV, d=8.0) and 20% inhibitory FS neurons (obtained by setting a=0.1, b=0.2, c = -65.0 mV, d=2.0). vpeak was set at 30 mV.