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Merge pull request #3220 from PrabhuUdurg/master
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Fix Izhikevich model equation on doc page
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jessica-mitchell authored Jun 20, 2024
2 parents c9bb064 + f5b5380 commit e0ea2a8
Showing 1 changed file with 6 additions and 8 deletions.
14 changes: 6 additions & 8 deletions models/izhikevich.h
Original file line number Diff line number Diff line change
Expand Up @@ -48,26 +48,24 @@ Implementation of the simple spiking neuron model introduced by Izhikevich
[1]_. The dynamics are given by:
.. math::
dV_m/dt &= 0.04 V_m^2 + 5 V_m + 140 - u + I
du/dt &= a (b V_m - u)
&dV_m/dt = 0.04 {V_m}^2 + 5 V_m + 140 - U_m + I \\
&du/dt = a (b V_m - U_m) \\
.. math::
&\text{if}\;\;\; V_m \geq V_{th}:\\
&\;\;\;\; V_m \text{ is set to } c\\
&\;\;\;\; u \text{ is incremented by } d\\
&\;\;\;\; U_m \text{ is incremented by } d\\
& \, \\
&v \text{ jumps on each spike arrival by the weight of the spike}
&V_m \text{ jumps on each spike arrival by the weight of the spike}
As published in [1]_, the numerics differs from the standard forward Euler
technique in two ways:
1) the new value of :math:`u` is calculated based on the new value of
1) the new value of :math:`U_m` is calculated based on the new value of
:math:`V_m`, rather than the previous value
2) the variable :math:`V_m` is updated using a time step half the size of that
used to update variable :math:`u`.
used to update variable :math:`U_m`.
This model offers both forms of integration, they can be selected using the
boolean parameter ``consistent_integration``. To reproduce some results
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