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.. currentmodule:: brian
.. index::
pair: example usage; plot
pair: example usage; run
pair: example usage; trace
pair: example usage; show
pair: example usage; Connection
pair: example usage; EmpiricalThreshold
pair: example usage; NeuronGroup
pair: example usage; Equations
pair: example usage; StateMonitor
.. _example-misc_COBAHH:
Example: COBAHH (misc)
======================
This is an implementation of a benchmark described
in the following review paper:
Simulation of networks of spiking neurons: A review of tools and strategies (2006).
Brette, Rudolph, Carnevale, Hines, Beeman, Bower, Diesmann, Goodman, Harris, Zirpe,
NatschlAger, Pecevski, Ermentrout, Djurfeldt, Lansner, Rochel, Vibert, Alvarez, Muller,
Davison, El Boustani and Destexhe.
Journal of Computational Neuroscience
Benchmark 3: random network of HH neurons with exponential synaptic conductances
Clock-driven implementation
(no spike time interpolation)
R. Brette - Dec 2007
70s for dt=0.1 ms with exponential Euler
::
from brian import *
# Parameters
area = 20000 * umetre ** 2
Cm = (1 * ufarad * cm ** -2) * area
gl = (5e-5 * siemens * cm ** -2) * area
El = -60 * mV
EK = -90 * mV
ENa = 50 * mV
g_na = (100 * msiemens * cm ** -2) * area
g_kd = (30 * msiemens * cm ** -2) * area
VT = -63 * mV
# Time constants
taue = 5 * ms
taui = 10 * ms
# Reversal potentials
Ee = 0 * mV
Ei = -80 * mV
we = 6 * nS # excitatory synaptic weight (voltage)
wi = 67 * nS # inhibitory synaptic weight
# The model
eqs = Equations('''
dv/dt = (gl*(El-v)+ge*(Ee-v)+gi*(Ei-v)-\
g_na*(m*m*m)*h*(v-ENa)-\
g_kd*(n*n*n*n)*(v-EK))/Cm : volt
dm/dt = alpham*(1-m)-betam*m : 1
dn/dt = alphan*(1-n)-betan*n : 1
dh/dt = alphah*(1-h)-betah*h : 1
dge/dt = -ge*(1./taue) : siemens
dgi/dt = -gi*(1./taui) : siemens
alpham = 0.32*(mV**-1)*(13*mV-v+VT)/ \
(exp((13*mV-v+VT)/(4*mV))-1.)/ms : Hz
betam = 0.28*(mV**-1)*(v-VT-40*mV)/ \
(exp((v-VT-40*mV)/(5*mV))-1)/ms : Hz
alphah = 0.128*exp((17*mV-v+VT)/(18*mV))/ms : Hz
betah = 4./(1+exp((40*mV-v+VT)/(5*mV)))/ms : Hz
alphan = 0.032*(mV**-1)*(15*mV-v+VT)/ \
(exp((15*mV-v+VT)/(5*mV))-1.)/ms : Hz
betan = .5*exp((10*mV-v+VT)/(40*mV))/ms : Hz
''')
P = NeuronGroup(4000, model=eqs,
threshold=EmpiricalThreshold(threshold= -20 * mV,
refractory=3 * ms),
implicit=True, freeze=True)
Pe = P.subgroup(3200)
Pi = P.subgroup(800)
Ce = Connection(Pe, P, 'ge', weight=we, sparseness=0.02)
Ci = Connection(Pi, P, 'gi', weight=wi, sparseness=0.02)
# Initialization
P.v = El + (randn(len(P)) * 5 - 5) * mV
P.ge = (randn(len(P)) * 1.5 + 4) * 10. * nS
P.gi = (randn(len(P)) * 12 + 20) * 10. * nS
# Record the number of spikes and a few traces
trace = StateMonitor(P, 'v', record=[1, 10, 100])
run(1 * second)
plot(trace[1])
plot(trace[10])
plot(trace[100])
show()
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