diff --git a/doc/htmldoc/synapses/index.rst b/doc/htmldoc/synapses/index.rst
index 855d398095..c4fedf12d4 100644
--- a/doc/htmldoc/synapses/index.rst
+++ b/doc/htmldoc/synapses/index.rst
@@ -9,7 +9,7 @@ Guides on using synapses in NEST
.. grid:: 1 1 2 2
- .. grid-item-card:: Managing coonnections
+ .. grid-item-card:: Managing coonnections
* :ref:`connectivity_concepts`
* :ref:`connection_generator`
diff --git a/models/iaf_bw_2001.h b/models/iaf_bw_2001.h
index f28ce10610..3efbace816 100644
--- a/models/iaf_bw_2001.h
+++ b/models/iaf_bw_2001.h
@@ -88,7 +88,7 @@ The membrane potential and synaptic variables evolve according to
I_\mathrm{NMDA} &= \frac{(V(t) - V_E)}{1+[\mathrm{Mg^{2+}}]\mathrm{exp}(-0.062V(t))/3.57}\sum_{j \in \Gamma_\mathrm{ex}}^{N_E}w_jS_{j,\mathrm{NMDA}}(t) \\[3ex]
I_\mathrm{GABA} &= (V(t) - V_I)\sum_{j \in \Gamma_\mathrm{in}}^{N_E}w_jS_{j,\mathrm{GABA}}(t) \\[5ex]
\frac{dS_{j,\mathrm{AMPA}}}{dt} &= -\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
- \frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
+ \frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
\frac{dS_{j,\mathrm{NMDA}}}{dt} &= -\frac{S_{j,\mathrm{NMDA}}}{\tau_\mathrm{NMDA,decay}} + \sum_{k \in \Delta_j} (k_0 + k_1 S(t)) \delta (t - t_j^k) \\[3ex]
where :math:`\Gamma_\mathrm{ex}` and :math:`\Gamma_\mathrm{in}` are index sets for presynaptic excitatory and inhibitory neurons respectively, and :math:`\Delta_j` is an index set for the spike times of neuron :math:`j`.
@@ -105,6 +105,8 @@ The specification of this model differs slightly from the one in [1]_. The param
:math:`g_\mathrm{GABA}`, and :math:`g_\mathrm{NMDA}` have been absorbed into the respective synaptic weights.
Additionally, the synapses from the external population are not separated from the recurrent AMPA-synapses.
+See also [2]_ and [3]_.
+
For more implementation details and a comparison to the exact version, see:
- `Brunel_Wang_2001_Model_Approximation <../model_details/Brunel_Wang_2001_Model_Approximation.ipynb>`_
@@ -118,16 +120,16 @@ The following parameters can be set in the status dictionary.
**Parameter** **Default** **Math equivalent** **Description**
=================== ================== ================================= ========================================================================
``E_L`` -70.0 mV :math:`E_\mathrm{L}` Leak reversal potential
-``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
-``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
-``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
+``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
+``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
+``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
``V_reset`` -60.0 mV :math:`V_\mathrm{reset}` Reset potential of the membrane
-``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
-``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
-``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
+``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
+``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
+``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
``tau_AMPA`` 2.0 ms :math:`\tau_\mathrm{AMPA}` Time constant of AMPA synapse
``tau_GABA`` 5.0 ms :math:`\tau_\mathrm{GABA}` Time constant of GABA synapse
-``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
+``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
``tau_decay_NMDA`` 100.0 ms :math:`\tau_\mathrm{NMDA,decay}` Decay time constant of NMDA synapse
``alpha`` 0.5 ms^{-1} :math:`\alpha` Rise-time coupling strength for NMDA synapse
``conc_Mg2`` 1.0 mM :math:`[\mathrm{Mg}^+]` Extracellular magnesium concentration
@@ -140,9 +142,9 @@ The following state variables evolve during simulation and are available either
**State variable** **Initial value** **Math equivalent** **Description**
================== ================= ========================== =================================
``V_m`` -70 mV :math:`V_{\mathrm{m}}` Membrane potential
-``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
-``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
-``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
+``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
+``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
+``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
``I_NMDA`` 0 pA :math:`I_\mathrm{NMDA}` NMDA current
``I_AMPA`` 0 pA :math:`I_\mathrm{AMPA}` AMPA current
``I_GABA`` 0 pA :math:`I_\mathrm{GABA}` GABA current
@@ -170,8 +172,14 @@ SpikeEvent, CurrentEvent, DataLoggingRequest
References
++++++++++
-.. [1] Wang, X.-J. (1999). Synaptic Basis of Cortical Persistent Activity: The Importance of NMDA Receptors to Working Memory. Journal of Neuroscience, 19(21), 9587–9603. https://doi.org/10.1523/JNEUROSCI.19-21-09587.1999
-.. [2] Brunel, N., & Wang, X.-J. (2001). Effects of Neuromodulation in a Cortical Network Model of Object Working Memory Dominated by Recurrent Inhibition. Journal of Computational Neuroscience, 11(1), 63–85. https://doi.org/10.1023/A:1011204814320
+.. [1] Wang, X.-J. (1999). Synaptic Basis of Cortical Persistent Activity: The
+ Importance of NMDA Receptors to Working Memory. Journal of Neuroscience,
+ 19(21), 9587–9603. https://doi.org/10.1523/JNEUROSCI.19-21-09587.1999
+
+.. [2] Brunel, N., & Wang, X.-J. (2001). Effects of Neuromodulation in a Cortical
+ Network Model of Object Working Memory Dominated by Recurrent Inhibition.
+ Journal of Computational Neuroscience, 11(1), 63–85. https://doi.org/10.1023/A:1011204814320
+
.. [3] Wang, X. J. (2002). Probabilistic decision making by slow reverberation in
cortical circuits. Neuron, 36(5), 955-968. https://doi.org/10.1016/S0896-6273(02)01092-9
diff --git a/models/iaf_bw_2001_exact.h b/models/iaf_bw_2001_exact.h
index 4d863a4440..c9c1bf50e2 100644
--- a/models/iaf_bw_2001_exact.h
+++ b/models/iaf_bw_2001_exact.h
@@ -87,7 +87,7 @@ The membrane potential and synaptic variables evolve according to
I_\mathrm{NMDA} &= \frac{(V(t) - V_E)}{1+[\mathrm{Mg^{2+}}]\mathrm{exp}(-0.062V(t))/3.57}\sum_{j \in
\Gamma_\mathrm{ex}}^{N_E}w_jS_{j,\mathrm{NMDA}}(t) \\[3ex]
I_\mathrm{GABA} &= (V(t) - V_I)\sum_{j \in \Gamma_\mathrm{in}}^{N_E}w_jS_{j,\mathrm{GABA}}(t) \\[5ex]
- \frac{dS_{j,\mathrm{AMPA}}}{dt} &=-\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
+ \frac{dS_{j,\mathrm{AMPA}}}{dt} &=-\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
\frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
\frac{dS_{j,\mathrm{NMDA}}}{dt} &= -\frac{S_{j,\mathrm{NMDA}}}{\tau_\mathrm{NMDA,decay}}+ \alpha x_j (1 - S_{j,\mathrm{NMDA}})\\[3ex]
\frac{dx_j}{dt} &= -\frac{x_j}{\tau_\mathrm{NMDA,rise}} + \sum_{k \in \Delta_j} \delta (t - t_j^k)
@@ -106,6 +106,8 @@ The specification of this model differs slightly from the one in [1]_. The param
Additionally, the synapses from the external population is not separated from the recurrent AMPA-synapses.
This model is slow to simulate when there are many neurons with NMDA-synapses, since each post-synaptic neuron simulates each pre-synaptic connection explicitly. The model :doc:`iaf_bw_2001 ` is an approximation to this model which is significantly faster.
+See also [2]_, [3]_
+
Parameters
++++++++++
@@ -115,16 +117,16 @@ The following parameters can be set in the status dictionary.
**Parameter** **Default** **Math equivalent** **Description**
=================== ================== ================================= ========================================================================
``E_L`` -70.0 mV :math:`E_\mathrm{L}` Leak reversal potential
-``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
-``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
-``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
+``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
+``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
+``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
``V_reset`` -60.0 mV :math:`V_\mathrm{reset}` Reset potential of the membrane
-``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
-``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
-``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
+``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
+``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
+``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
``tau_AMPA`` 2.0 ms :math:`\tau_\mathrm{AMPA}` Time constant of AMPA synapse
``tau_GABA`` 5.0 ms :math:`\tau_\mathrm{GABA}` Time constant of GABA synapse
-``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
+``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
``tau_decay_NMDA`` 100.0 ms :math:`\tau_\mathrm{NMDA,decay}` Decay time constant of NMDA synapse
``alpha`` 0.5 ms^{-1} :math:`\alpha` Rise-time coupling strength for NMDA synapse
``conc_Mg2`` 1.0 mM :math:`[\mathrm{Mg}^+]` Extracellular magnesium concentration
@@ -137,9 +139,9 @@ The following state variables evolve during simulation and are available either
**State variable** **Initial value** **Math equivalent** **Description**
================== ================= ========================== =================================
``V_m`` -70 mV :math:`V_{\mathrm{m}}` Membrane potential
-``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
-``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
-``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
+``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
+``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
+``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
``I_NMDA`` 0 pA :math:`I_\mathrm{NMDA}` NMDA current
``I_AMPA`` 0 pA :math:`I_\mathrm{AMPA}` AMPA current
``I_GABA`` 0 pA :math:`I_\mathrm{GABA}` GABA current
diff --git a/models/iaf_psc_exp.h b/models/iaf_psc_exp.h
index 0fc324a0ab..caab9f74e0 100644
--- a/models/iaf_psc_exp.h
+++ b/models/iaf_psc_exp.h
@@ -135,6 +135,9 @@ on the synaptic time constant according to
will numerically behave as if ``tau_m`` is equal to ``tau_syn_ex`` or
``tau_syn_in``, respectively, to avoid numerical instabilities.
+ NEST uses exact integration [2]_, [3]_ to integrate subthreshold membrane dynamics
+ with maximum precision.
+
For implementation details see the
`IAF Integration Singularity notebook <../model_details/IAF_Integration_Singularity.ipynb>`_.
diff --git a/pynest/examples/wang_decision_making.py b/pynest/examples/wang_decision_making.py
index 764e18b537..16d712b43d 100644
--- a/pynest/examples/wang_decision_making.py
+++ b/pynest/examples/wang_decision_making.py
@@ -36,8 +36,8 @@
References
~~~~~~~~~~
.. [1] Wang X-J (2002). Probabilistic Decision Making by Slow Reverberation in
-Cortical Circuits. Neuron, Volume 36, Issue 5, Pages 955-968.
-https://doi.org/10.1016/S0896-6273(02)01092-9.
+ Cortical Circuits. Neuron, Volume 36, Issue 5, Pages 955-968.
+ https://doi.org/10.1016/S0896-6273(02)01092-9.
"""