/usr/share/pyshared/brian/library/IF.py is in python-brian 1.3.1-1build1.
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Integrate-and-Fire models.
'''
from brian.units import *
from brian.stdunits import *
from brian.membrane_equations import *
from numpy import exp
__all__ = ['leaky_IF', 'perfect_IF', 'exp_IF', 'quadratic_IF', 'Brette_Gerstner', 'Izhikevich', \
'AdaptiveReset', 'aEIF']
__credits__ = dict(author='Romain Brette (brette@di.ens.fr)',
date='April 2008')
#TODO: specific integration methods
"""
******************************************
One-dimensional integrate-and-fire models
******************************************
"""
@check_units(tau=second, El=volt)
def leaky_IF(tau, El):
'''
A leaky integrate-and-fire model (membrane equation).
tau dvm/dt = EL - vm
'''
return MembraneEquation(tau) + \
Current('Im=El-vm:volt', current_name='Im', El=El)
@check_units(tau=second)
def perfect_IF(tau):
'''
A perfect integrator.
tau dvm/dt = ...
'''
return MembraneEquation(tau)
@check_units(C=farad, gL=siemens, EL=volt, VT=volt, DeltaT=volt)
def exp_IF(C, gL, EL, VT, DeltaT):
'''
An exponential integrate-and-fire model (membrane equation).
'''
return MembraneEquation(C) + \
Current('Im=gL*(EL-vm)+gL*DeltaT*exp((vm-VT)/DeltaT):amp', \
gL=gL, EL=EL, DeltaT=DeltaT, exp=exp, VT=VT)
@check_units(C=farad, a=siemens / volt, EL=volt, VT=volt)
def quadratic_IF(C, a, EL, VT):
'''
Quadratic integrate-and-fire model.
C*dvm/dt=a*(vm-EL)*(vm-VT)
'''
return MembraneEquation(C) + \
Current('Im=a*(vm-EL)*(vm-VT):amp', \
a=a, EL=EL, exp=exp, VT=VT)
"""
******************************************
Two-dimensional integrate-and-fire models
******************************************
"""
@check_units(a=1 / second, b=1 / second)
def Izhikevich(a=0.02 / ms, b=0.2 / ms):
'''
Returns a membrane equation for the Izhikevich model
(variables: vm and w).
'''
return MembraneEquation(1.) + \
Current('''
Im=(0.04/ms/mV)*vm**2+(5/ms)*vm+140*mV/ms-w : volt/second
dw/dt=a*(b*vm-w) : volt/second
''', current_name='Im')
@check_units(C=farad, gL=siemens, EL=volt, VT=volt, DeltaT=volt, \
tauw=second, a=siemens)
def Brette_Gerstner(C=281 * pF, gL=30 * nS, EL= -70.6 * mV, VT= -50.4 * mV, \
DeltaT=2 * mV, tauw=144 * ms, a=4 * nS):
'''
Returns a membrane equation for the Brette-Gerstner model.
Default: a regular spiking cortical cell.
Brette, R. and W. Gerstner (2005).
Adaptive exponential integrate-and-fire model as an effective
description of neuronal activity.
Journal of Neurophysiology 94: 3637-3642.
'''
return exp_IF(C, gL, EL, VT, DeltaT) + \
IonicCurrent('dw/dt=(a*(vm-EL)-w)/tauw:amp', \
a=a, EL=EL, tauw=tauw)
aEIF = Brette_Gerstner # synonym
AdEx = aEIF
class AdaptiveReset(object):
'''
A two-variable reset:
V<-Vr
w<-w+b
(used in Izhikevich and Brette-Gerstner models)
'''
def __init__(self, Vr= -70.6 * mvolt, b=0.0805 * nA):
self.Vr = Vr
self.b = b
def __call__(self, P):
'''
Clamps membrane potential at reset value.
'''
spikes = P.LS.lastspikes()
P.vm_[spikes] = self.Vr
P.w_[spikes] += self.b
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