Subsections

• Equations
• Default values

   
LIM model equations

Equations

The temporal evolution of the potential and the threshold of NBC neurons in a network of N neurons takes place according to the following equations:

V_i(t)=V_i(t-1)(1-($${\frac{\Delta t}{\tau_{V}}}$$+$${\frac{\Delta t \times U_{rest}}{\tau_{V}}}$$)

$\theta$[y] is the Heaviside step function

$$\theta$$[y] = $$\left\{\vphantom{ \begin{array}{ll} 0 & if\;y < 0 \\ 1 & otherwise \end{array}}\right.$$$$\begin{array}{ll} 0 & if\;y < 0 \\ 1 & otherwise \end{array}$$ $$\left.\vphantom{ \begin{array}{ll} 0 & if\;y < 0 \\ 1 & otherwise \end{array}}\right.$$

U_rest,  U(0),  $\tau_{V}^{}$,  V_pspMax,  s_rest,  S_A,  $\tau_{s}^{}$ are the parameters which are set at the beginning of each simulation.

The threshold equation shows that the value of the threshold of a neuron at a given time tdepends on the firing history of the neuron. In fact by replacing F, the following expression for the threshold of a neuron which has fired pspikes, the kth spike happening at time T_k, is obtained:

s(t)=s_rest(1+e^{- ${\frac{t-T_{1}}{\tau_{s}}}$})+S_Ae^{- ${\frac{t}{\tau_{s}}}$} $$\sum_{k=1}^{p}$$e^{${\frac{T_{k}}{\tau_{s}}}$}

Default values

These are the default values of a Leaky Integrator Model as stored in the .L_unit file:

ModelType: L
RestPotential: -70.0000
TimeCsteMbPot: 10.0000
Threshold: -65.0000
EpspSize: 0.5000
IpspSize: 0.0000
NoiseMean: 0.0000
NoiseSd: 0.0000
NoiseFilter: 0
Capacity: 1.0000000000
TimeStep: 1.000
PostSpikePotential: -85.0000
Adaptation: 20.0000
E_K: -90.0000
E_Na: 65.0000
PosReversalPot: 0.0000
NegReversalPot: -90.0000
TimeCsteThreshold: 20.0000
EpspSd: 0.0000
IpspSd: 0.0000
FilterResistance: 10.000
Fatigue: 0.000
LessFatigue: 0

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