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The Model Neuron

Starting with the coherence layer, network operations are simulated in detail, with spiking integrate-and-fire neurons described by

C\, \frac{dV}{dt}=-V/R+I(t)\, \, .
\end{displaymath} (10)

Here, the parameter \( C\) models the membrane capacity of the neuron, and \( R \) is the corresponding membrane resistance. In the simulations, the membrane capacity is fixed to \( C=0.00625 \) , and \( R=40 \) for all neurons. This gives a membrane time constant of \( \tau =0.25 \).

In an integrate-and-fire neuron, the membrane potential \( V(t) \) develops according to equation (10) as long as \( V<\theta \), the threshold potential. If \( \theta =16.8 \) is reached, an actionpotential or spike is emitted, and the membrane potential is reset to \( V=0 \). After a short refractory period, \( t_{r}=0.2 \), where \( V(t) \) stays at its resting level \( V_{0}=0 \), the membrane potential develops again according to Equation 10. If a neuron \( k \) fired at times \( t_{k}^{F} \), it supplies a current of exponentially decaying pulses, \( i_{k}(t;\tau )=\sum _{t^{F}}\exp (-(t-t_{k}^{F})/\tau ) \), to all postsynaptic neurons.