iaf_psc_delta – Leaky integrateandfire model with deltashaped input currents¶
Description¶
iaf_psc_delta
is a leaky integrateandfire neuron model with
a hard threshold,
a fixed refractory period,
Dirac delta (\(\delta\))shaped synaptic input currents.
Membrane potential evolution, spike emission, and refractoriness¶
The membrane potential evolves according to
where the derivative of change in voltage due to synaptic input \(\dot{\Delta}_{\text{syn}}(t)\) is discussed below and \(I_\text{e}\) is a constant input current set as a model parameter.
A spike is emitted at time step \(t^*=t_{k+1}\) if
Subsequently,
that is, the membrane potential is clamped to \(V_{\text{reset}}\) during the refractory period.
Synaptic input¶
The change in membrane potential due to synaptic inputs can be formulated as:
where \(j\) indexes either excitatory (\(w_j > 0\)) or inhibitory (\(w_j < 0\)) presynaptic neurons, \(k\) indexes the spike times of neuron \(j\), \(d_j\) is the delay from neuron \(j\), and \(\delta\) is the Dirac delta distribution. This implies that the jump in voltage upon a single synaptic input spike is
where \(w\) is the corresponding synaptic weight in mV.
The change in voltage caused by the synaptic input can be interpreted as being caused by individual postsynaptic currents (PSCs) given by
As a consequence, the total charge \(q\) transferred by a single PSC is
By default, \(V_\text{m}\) is not bounded from below. To limit hyperpolarization to biophysically plausible values, set parameter \(V_{\text{min}}\) as lower bound of \(V_\text{m}\).
Note
Spikes arriving while the neuron is refractory, are discarded by
default. If the property refractory_input
is set to True, such
spikes are added to the membrane potential at the end of the
refractory period, dampened according to the interval between
arrival and end of refractoriness.
Parameters¶
The following parameters can be set in the status dictionary.
Parameter 
Default 
Math equivalent 
Description 


70 mV 
\(E_\text{L}\) 
Resting membrane potential 

250 pF 
\(C_{\text{m}}\) 
Capacitance of the membrane 

10 ms 
\(\tau_{\text{m}}\) 
Membrane time constant 

2 ms 
\(t_{\text{ref}}\) 
Duration of refractory period 

55 mV 
\(V_{\text{th}}\) 
Spike threshold 

70 mV 
\(V_{\text{reset}}\) 
Reset potential of the membrane 

0 pA 
\(I_\text{e}\) 
Constant input current 

\(\infty\) mV 
\(V_{\text{min}}\) 
Absolute lower value for the membrane potential 


None 
If set to True, spikes arriving during refractory period are integrated afterwards 
References¶
Sends¶
SpikeEvent
Receives¶
SpikeEvent, CurrentEvent, DataLoggingRequest