How to simulate COBA synapse and Izhikevich neuron in Brian 2?
Xu Zhang
I'm trying to build a simple SNN in Brian 2 using the same neuron model and synapse model in CarlSim, which is a C++ simulator of SNNs. But I can't make them to fire even fire with similar frequencies given the same inputs. Below is the synapse model described in CarlSim's Website. After that is my brian 2 code for modeling the 4 parameters Izhikevich neuron and this COBA synapse.
from brian2 import *import numpy
import matplotlib
from matplotlib import pylab, mlab, pyplot
np = numpy
plt = pyplot
from IPython.display import display
from IPython.core.pylabtools import figsize, getfigs
from pylab import *
from numpy import *
from brian2 import PopulationRateMonitor
import timeit
plt.close('all')
start_scope()
start = timeit.default_timer()
dt = 0.5*ms # simulation time step
tauAP = 5*ms # synaptic time constant (ms)
tauNM=150*ms
vrevAMPA=0
vNMDArev=0
eqs = '''
dv/dt = (0.04*v**2 + 5*v + 140 - u -Ie+Iinj)/ms : 1
du/dt = a*(b*v - u)/ms : 1
dgAMPA/dt = -gAMPA/tauAP : 1
dgNMDA/dt = -gNMDA/tauNM : 1
Ie = gAMPA*(v-vrevAMPA)+gNMDA*((((v+80)/(60.0))**2/(1+((v+80)/(60.0))**2)))*(v-vNMDArev) : 1
Iinj : 1
a : 1
b : 1
c : 1
d : 1
'''
N = 7
G = NeuronGroup(N, eqs, clock=Clock(dt), threshold = 'v >= 30', reset = '''
v = c
u = u + d
''')
G.a = 0.02
G.b = 0.2
G.c = -65.0
G.d = 8.0
G.v = -65.0
G.u = G.b*(G.v)
G.gAMPA=0
G.gNMDA=0
'''inputcase=[[0,0,3,0],[0, 0, 0, 3],[0, 3, 3, 0],[0, 3, 0, 3],[3, 0, 3, 0],[3, 0, 0, 3]];
targOut=[[120,0],[0,120],[0,120],[0,120],[120,0],[120,0]]'''
N1pre=0
N2pre=0
N3pre=0
N4pre=0
N5pre=0
'''figure(figsize=(10,4))
plot(rmsetot[1:-1])
xlabel('Test epoch')
ylabel('RMSE')'''
N6pre=0
N7pre=0
'''print(inputcase[1][:])'''
S = Synapses(G, G,'w : 1', pre='''gAMPA+= w
gNMDA+=w''')
S.connect(0,2)
S.connect(1,2)
S.connect(2,3)
S.connect(2,4)
S.connect(0,5)
S.connect(1,6)
S.connect(3,5)
S.connect(4,6)
#S.w = '0.5'
S.delay[:] = '1*ms'
S.w=[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0]
def visualise_connectivity(S):
figure(figsize=(10,4))
plot([2,5,3,4,2,5],[5,5,3,3,1,1],'ok',ms=20)
plot(3.5,4,'or',ms=20)
plot([2,3.5],[5,4],'-k')
plot([5,3.5],[5,4],'-k')
plot([3.5,3],[4,3],'-r')
plot([3.5,4],[4,3],'-r')
plot([3,2],[3,1],'-k')
plot([4,5],[3,1],'-k')
plot([2,2],[5,1],'-k')
plot([5,5],[5,1],'-k')
xlim(1,6)
ylim(0,6)
'''def visualise_connectivity(S):
Ns = len(S.source)
Nt = len(S.target)
figure(figsize=(10, 4))
subplot(121)
plot(zeros(Ns), arange(Ns), 'ok', ms=10)
plot(ones(Nt), arange(Nt), 'ok', ms=10)
for i, j in zip(S.i, S.j):
plot([0, 1], [i, j], '-k')
xticks([0, 1], ['Source', 'Target'])
ylabel('Neuron index')
xlim(-0.1, 1.1)
ylim(-1, max(Ns, Nt))
subplot(122)
plot(S.i, S.j, 'ok')
xlim(-1, Ns)
ylim(-1, Nt)
xlabel('Source neuron index')
ylabel('Target neuron index')'''
#visualise_connectivity(S)
#plt.show()
M = StateMonitor(G, 'v', record=True)
spikemon = SpikeMonitor(G)
R = PopulationRateMonitor(G)
rmsepre=[]
rmsepost=[]
rmsetot=[]
rmsePre=3000
learningR=0.15
Tmax=1000.0
G.Iinj=[0, 0, 0, 4, 0, 0, 0];
print('length of spikemon is %d',len(spikemon))
run(Tmax*ms)
print('length of spikemon is %d',len(spikemon))
stop = timeit.default_timer()
print stop - start
figure(1)
plot(spikemon.t/ms, spikemon.i, '.k')
xlabel('Time (ms)')
ylabel('Neuron index')
title('Excitatory Neurons')
show()
Dan Goodman
If you have equivalent equations it should give the same results. One
thing that is difficult to get right with the Izhikevich neuron is the
units, since Brian insists on it being dimensionally consistent (which
the standard formulation of the Izhikevich neuron is not).
You might try this as a starting point (Brian 1 code, but easily
converted to Brian 2):
https://github.com/brian-team/brian/blob/master/dev/unfinished_examples/frompapers/Izhikevich_2006_Polychronization.py
Dan
On 18/12/2015 19:17, Xu Zhang wrote:
> I'm trying to build a simple SNN in Brian 2 using the same neuron model
> and synapse model in CarlSim, which is a C++ simulator of SNNs. But I
> can't make them to fire even fire with similar frequencies given the
> same inputs. Below is the synapse model described in CarlSim's Website.
> After that is my brian 2 code for modeling the 4 parameters Izhikevich
> neuron and this COBA synapse.
>
>
>
> from brian2 import *
>
> import numpy
>
> import matplotlib
>
> from matplotlib import pylab, mlab, pyplot
>
> np = numpy
>
> plt = pyplot
>
> from IPython.display import display
>
> from IPython.core.pylabtools import figsize, getfigs
>
> from pylab import *
>
> from numpy import *
>
> from brian2 import PopulationRateMonitor
>
> import timeit
>
> plt.close('all')
>
>
> start_scope()
>
> start = timeit.default_timer()
>
>
>
> tauAP = 5*ms# synaptic time constant (ms)
> http://www.facebook.com/briansimulator
> https://twitter.com/briansimulator
>
> New paper about Brian 2: Stimberg M, Goodman DFM, Benichoux V, Brette R
> (2014).Equation-oriented specification of neural models for simulations.
> Frontiers Neuroinf, doi: 10.3389/fninf.2014.00006.
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Xu Zhang
> <mailto:briansupport+unsub...@googlegroups.com>.
Dan Goodman
alpha synapse it's a straightforward ODE. Just make sure the constants
are the same and the behaviour should be equivalent unless you're
getting numerical instability issues (in which case, try different
solvers and/or reducing the time step dt).
Dan
> > https://twitter.com/briansimulator
> >
> > New paper about Brian 2: Stimberg M, Goodman DFM, Benichoux V,
> Brette R
> > (2014).Equation-oriented specification of neural models for
> simulations.
> > Frontiers Neuroinf, doi: 10.3389/fninf.2014.00006.
> > ---
> > You received this message because you are subscribed to the Google
> > Groups "Brian" group.
> > To unsubscribe from this group and stop receiving emails from it,
> send
> > <mailto:briansupport...@googlegroups.com <javascript:>>.
> > <mailto:brians...@googlegroups.com <javascript:>>.
> --
> http://www.facebook.com/briansimulator
> https://twitter.com/briansimulator
>
> New paper about Brian 2: Stimberg M, Goodman DFM, Benichoux V, Brette R
> (2014).Equation-oriented specification of neural models for simulations.
> Frontiers Neuroinf, doi: 10.3389/fninf.2014.00006.
> ---
> You received this message because you are subscribed to the Google
> Groups "Brian" group.
> To unsubscribe from this group and stop receiving emails from it, send
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