Table 1.

List of the functions describing the phenomenological neuron model used in the spiking neural network.

Learning function	if Δ t ≤ 0	$\begin{array}{l}W(\Delta t)=\eta \cdot \exp (\Delta t/t_{\text{syn}})\\ \times [A_{+}(1-\Delta t/{\tilde{\tau }}_{+})\\ +A_{-}\cdot (1-\Delta t/{\tilde{\tau }}_{-})]\end{array}$
	f Δ t>0	$W(\Delta t)=\eta \cdot [-A_{+}\cdot \Delta t/{\tilde{\tau }}_{+}-A_{-}\cdot \Delta t/{\tilde{\tau }}_{-}]$
Kernel function	$\frac{1}{1-\frac{{\tau }_{\text{m}}}{{\tau }_{\text{s}}}}\cdot [\exp (-t_{\text{i}}/{\tau }_{\text{s}})-\exp (-t_{\text{i}}/{\tau }_{\text{m}})]$
Refractory function	−ϑ exp(−tr/τ)

The different τ’s appearing in the definitions are time constants, A_± are constant parameters and θ is the neuron threshold.