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12 | 12 | # |
13 | 13 | # .. math:: |
14 | 14 | # |
15 | | -# C_m \frac{dV_m}{dt} = |
16 | | -# -g_L(V_m-E_L)+g_L\Delta_T\exp\left(\frac{V_m-V_{th}}{\Delta_T}\right) - g_e(t)(V_m-E_e) \\ |
17 | | -# -g_i(t)(V_m-E_i)-w +I_e |
| 15 | +# C_m \frac{dV_m}{dt} = |
| 16 | +# -g_L(V_m-E_L)+g_L\Delta_T\exp\left(\frac{V_m-V_{th}}{\Delta_T}\right) - g_e(t)(V_m-E_e) \\ |
| 17 | +# -g_i(t)(V_m-E_i)-w +I_e |
18 | 18 | # |
19 | 19 | # and |
20 | 20 | # |
21 | 21 | # .. math:: |
22 | 22 | # |
23 | | -# \tau_w \frac{dw}{dt} = a(V_m-E_L) - w |
| 23 | +# \tau_w \frac{dw}{dt} = a(V_m-E_L) - w |
24 | 24 | # |
25 | 25 | # Note that the membrane potential can diverge to positive infinity due to the exponential term. To avoid numerical instabilities, instead of :math:`V_m`, the value :math:`\min(V_m,V_{peak})` is used in the dynamical equations. |
26 | 26 | # |
27 | 27 | # .. note:: |
28 | 28 | # |
29 | | -# The default refractory period for ``aeif`` models is zero, consistent with the model definition in |
30 | | -# Brette & Gerstner [1]_. Thus, an ``aeif`` neuron with default parameters can fire multiple spikes in a single |
31 | | -# time step, which can lead to exploding spike numbers and extreme slow-down of simulations. |
32 | | -# To avoid such unphysiological behavior, you should set a refractory time ``refr_t > 0``. |
| 29 | +# The default refractory period for ``aeif`` models is zero, consistent with the model definition in |
| 30 | +# Brette & Gerstner [1]_. Thus, an ``aeif`` neuron with default parameters can fire multiple spikes in a single |
| 31 | +# time step, which can lead to exploding spike numbers and extreme slow-down of simulations. |
| 32 | +# To avoid such unphysiological behavior, you should set a refractory time ``refr_t > 0``. |
33 | 33 | # |
34 | 34 | # |
35 | 35 | # References |
36 | 36 | # ++++++++++ |
37 | 37 | # |
38 | 38 | # .. [1] Brette R and Gerstner W (2005). Adaptive exponential |
39 | | -# integrate-and-fire model as an effective description of neuronal |
40 | | -# activity. Journal of Neurophysiology. 943637-3642 |
41 | | -# DOI: https://doi.org/10.1152/jn.00686.2005 |
| 39 | +# integrate-and-fire model as an effective description of neuronal |
| 40 | +# activity. Journal of Neurophysiology. 943637-3642 |
| 41 | +# DOI: https://doi.org/10.1152/jn.00686.2005 |
42 | 42 | # |
43 | 43 | # |
44 | 44 | # See also |
|
47 | 47 | # iaf_cond_exp, aeif_cond_alpha |
48 | 48 | # |
49 | 49 | # |
| 50 | +# Copyright statement |
| 51 | +# +++++++++++++++++++ |
| 52 | +# |
| 53 | +# This file is part of NEST. |
| 54 | +# |
| 55 | +# Copyright (C) 2004 The NEST Initiative |
| 56 | +# |
| 57 | +# NEST is free software: you can redistribute it and/or modify |
| 58 | +# it under the terms of the GNU General Public License as published by |
| 59 | +# the Free Software Foundation, either version 2 of the License, or |
| 60 | +# (at your option) any later version. |
| 61 | +# |
| 62 | +# NEST is distributed in the hope that it will be useful, |
| 63 | +# but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 64 | +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 65 | +# GNU General Public License for more details. |
| 66 | +# |
| 67 | +# You should have received a copy of the GNU General Public License |
| 68 | +# along with NEST. If not, see <http://www.gnu.org/licenses/>. |
| 69 | +# |
| 70 | +# |
50 | 71 | model aeif_cond_exp_neuron: |
51 | 72 |
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52 | 73 | state: |
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